\documentclass[9pt]{article}
\usepackage{amsmath}
\begin{document}
Read in the following dictionary:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{16}   &  0.0 & +  7.00 x_{1} & -7.00 x_{2} & +  4.00 x_{3} & -1.00 x_{4} & -8.00 x_{5} & +  6.00 x_{6} & -10.00 x_{7} & -10.00 x_{8} & + 10.00 x_{9} & -6.00 x_{10} & -9.00 x_{11} & +  1.00 x_{12} & +  5.00 x_{13} &   & -2.00 x_{15}\\
 x_{17}   &  57.0 & -7.00 x_{1} & -7.00 x_{2} & -7.00 x_{3} & + 10.00 x_{4} & -6.00 x_{5} & -8.00 x_{6} & +  4.00 x_{7} & -7.00 x_{8} & +  6.00 x_{9} & +  4.00 x_{10} & -10.00 x_{11} & -2.00 x_{12} & -9.00 x_{13} & +  8.00 x_{14} & -9.00 x_{15}\\
 x_{18}   &  -1.0 & +  4.00 x_{1} & +  9.00 x_{2} & -3.00 x_{3} & +  5.00 x_{4} & +  8.00 x_{5} & +  8.00 x_{6} & +  9.00 x_{7} & -1.00 x_{8} & +  4.00 x_{9} & -3.00 x_{10} & -9.00 x_{11} & +  5.00 x_{12} & -4.00 x_{13} & -4.00 x_{14} & -5.00 x_{15}\\
 x_{19}   &  0.0 & -1.00 x_{1} & -7.00 x_{2} & +  2.00 x_{3} & +  7.00 x_{4} & +  4.00 x_{5} & +  9.00 x_{6} & -3.00 x_{7} & -5.00 x_{8} & -2.00 x_{9} & +  3.00 x_{10} &   & -3.00 x_{12} & +  8.00 x_{13} & -4.00 x_{14} & +  2.00 x_{15}\\
 x_{20}   &  -64.0 & +  4.00 x_{1} & +  5.00 x_{2} & + 10.00 x_{3} & +  1.00 x_{4} &   & -3.00 x_{6} & +  5.00 x_{7} & +  8.00 x_{8} & +  5.00 x_{9} & -3.00 x_{10} & +  8.00 x_{11} & -3.00 x_{12} & -5.00 x_{13} & +  6.00 x_{14} & +  7.00 x_{15}\\
 x_{21}   &  -15.0 & +  9.00 x_{1} & +  4.00 x_{2} & + 10.00 x_{3} & +  4.00 x_{4} & -6.00 x_{5} & -2.00 x_{6} & +  6.00 x_{7} & +  6.00 x_{8} & -4.00 x_{9} & -4.00 x_{10} & +  1.00 x_{11} & -10.00 x_{12} & -8.00 x_{13} & +  3.00 x_{14} & + 10.00 x_{15}\\
 x_{22}   &  20.0 & +  1.00 x_{1} & -9.00 x_{2} & +  3.00 x_{3} & +  7.00 x_{4} & +  4.00 x_{5} & -10.00 x_{6} & +  5.00 x_{7} &   & -4.00 x_{9} & + 10.00 x_{10} & -10.00 x_{11} & +  2.00 x_{12} & +  1.00 x_{13} & -7.00 x_{14} &   \\
 x_{23}   &  107.0 & -9.00 x_{1} & +  6.00 x_{2} & -8.00 x_{3} & -6.00 x_{4} & +  9.00 x_{5} & +  1.00 x_{6} & +  2.00 x_{7} & -2.00 x_{8} & -1.00 x_{9} & -3.00 x_{10} & -1.00 x_{11} & -4.00 x_{12} & +  4.00 x_{13} & -3.00 x_{14} & -10.00 x_{15}\\
 x_{24}   &  117.0 & +  2.00 x_{1} & -1.00 x_{2} & -7.00 x_{3} & -7.00 x_{4} & +  4.00 x_{5} & -6.00 x_{6} & -10.00 x_{7} & -8.00 x_{8} & -3.00 x_{9} & +  3.00 x_{10} & +  9.00 x_{11} & -1.00 x_{12} & +  4.00 x_{13} & -8.00 x_{14} & -9.00 x_{15}\\
 x_{25}   &  29.0 & -1.00 x_{1} & -8.00 x_{2} & +  3.00 x_{3} & +  7.00 x_{4} & + 10.00 x_{5} & -10.00 x_{6} & +  7.00 x_{7} & -10.00 x_{8} & +  4.00 x_{9} & +  2.00 x_{10} & +  5.00 x_{11} & -5.00 x_{12} & +  9.00 x_{13} & -7.00 x_{14} & +  5.00 x_{15}\\
 x_{26}   &  -6.0 & +  4.00 x_{1} & -3.00 x_{2} & +  1.00 x_{3} & +  1.00 x_{4} & +  5.00 x_{5} & -5.00 x_{6} & +  3.00 x_{7} & -10.00 x_{8} & -6.00 x_{9} & +  1.00 x_{10} & -3.00 x_{11} & +  7.00 x_{12} & +  7.00 x_{13} & +  6.00 x_{14} & +  7.00 x_{15}\\
 x_{27}   &  -2.0 & +  5.00 x_{1} & +  5.00 x_{2} & +  5.00 x_{3} & +  6.00 x_{4} & -9.00 x_{5} & -2.00 x_{6} & -2.00 x_{7} & +  6.00 x_{8} & +  6.00 x_{9} & +  2.00 x_{10} & +  3.00 x_{11} & -8.00 x_{12} & -9.00 x_{13} & +  3.00 x_{14} & +  7.00 x_{15}\\
 x_{28}   &  41.0 & -9.00 x_{1} & +  5.00 x_{2} & -4.00 x_{3} & +  5.00 x_{4} & -7.00 x_{5} & +  1.00 x_{6} &   & -5.00 x_{8} & -1.00 x_{9} & -4.00 x_{10} & -1.00 x_{11} & -2.00 x_{12} & +  9.00 x_{13} & +  1.00 x_{14} & +  5.00 x_{15}\\
 x_{29}   &  -5.0 & +  3.00 x_{1} & -3.00 x_{2} & -5.00 x_{3} & -9.00 x_{4} & -8.00 x_{5} & +  3.00 x_{6} & +  4.00 x_{7} & -5.00 x_{8} &   & +  6.00 x_{10} & +  1.00 x_{11} & -7.00 x_{12} & +  2.00 x_{13} & +  9.00 x_{14} & -4.00 x_{15}\\
 x_{30}   &  4.0 & -9.00 x_{1} & -1.00 x_{2} & -9.00 x_{3} & -4.00 x_{4} & +  7.00 x_{5} & +  9.00 x_{6} & -7.00 x_{7} & + 10.00 x_{8} & +  4.00 x_{9} & -5.00 x_{10} & -7.00 x_{11} & + 10.00 x_{12} & -7.00 x_{13} & -3.00 x_{14} &   \\
 x_{31}   &  32.0 & -6.00 x_{1} & +  3.00 x_{2} & -4.00 x_{3} & +  2.00 x_{4} & -8.00 x_{5} & +  2.00 x_{6} & -10.00 x_{7} & -5.00 x_{8} & -2.00 x_{9} & +  9.00 x_{10} & +  4.00 x_{11} & -3.00 x_{12} & -2.00 x_{13} & -3.00 x_{14} & +  4.00 x_{15}\\
\hline
z    &  0.0 & -4.00 x_{1} & -1.00 x_{2} &   & +  3.00 x_{4} & -1.00 x_{5} & -4.00 x_{6} & +  1.00 x_{7} & -3.00 x_{8} & -3.00 x_{9} & -4.00 x_{10} & -5.00 x_{11} & +  1.00 x_{12} & -2.00 x_{13} & -2.00 x_{14} & +  2.00 x_{15}\\
\end{array}\]
\subsection{Initialization Phase: Dual Problem Solving}
New Objective in primal was changed to : \[ \max\ \sum_{j=1}^{15}\ - x_j \] 
Primal variable $x_j$ corresponds to dual variable $y_j$ for $j = 1,\ldots,31$
Dual Dictionary (with objective changed is): 
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{1}   &  1.0 & -7.00 y_{16} & +  7.00 y_{17} & -4.00 y_{18} & +  1.00 y_{19} & -4.00 y_{20} & -9.00 y_{21} & -1.00 y_{22} & +  9.00 y_{23} & -2.00 y_{24} & +  1.00 y_{25} & -4.00 y_{26} & -5.00 y_{27} & +  9.00 y_{28} & -3.00 y_{29} & +  9.00 y_{30} & +  6.00 y_{31}\\
 y_{2}   &  1.0 & +  7.00 y_{16} & +  7.00 y_{17} & -9.00 y_{18} & +  7.00 y_{19} & -5.00 y_{20} & -4.00 y_{21} & +  9.00 y_{22} & -6.00 y_{23} & +  1.00 y_{24} & +  8.00 y_{25} & +  3.00 y_{26} & -5.00 y_{27} & -5.00 y_{28} & +  3.00 y_{29} & +  1.00 y_{30} & -3.00 y_{31}\\
 y_{3}   &  1.0 & -4.00 y_{16} & +  7.00 y_{17} & +  3.00 y_{18} & -2.00 y_{19} & -10.00 y_{20} & -10.00 y_{21} & -3.00 y_{22} & +  8.00 y_{23} & +  7.00 y_{24} & -3.00 y_{25} & -1.00 y_{26} & -5.00 y_{27} & +  4.00 y_{28} & +  5.00 y_{29} & +  9.00 y_{30} & +  4.00 y_{31}\\
 y_{4}   &  1.0 & +  1.00 y_{16} & -10.00 y_{17} & -5.00 y_{18} & -7.00 y_{19} & -1.00 y_{20} & -4.00 y_{21} & -7.00 y_{22} & +  6.00 y_{23} & +  7.00 y_{24} & -7.00 y_{25} & -1.00 y_{26} & -6.00 y_{27} & -5.00 y_{28} & +  9.00 y_{29} & +  4.00 y_{30} & -2.00 y_{31}\\
 y_{5}   &  1.0 & +  8.00 y_{16} & +  6.00 y_{17} & -8.00 y_{18} & -4.00 y_{19} &   & +  6.00 y_{21} & -4.00 y_{22} & -9.00 y_{23} & -4.00 y_{24} & -10.00 y_{25} & -5.00 y_{26} & +  9.00 y_{27} & +  7.00 y_{28} & +  8.00 y_{29} & -7.00 y_{30} & +  8.00 y_{31}\\
 y_{6}   &  1.0 & -6.00 y_{16} & +  8.00 y_{17} & -8.00 y_{18} & -9.00 y_{19} & +  3.00 y_{20} & +  2.00 y_{21} & + 10.00 y_{22} & -1.00 y_{23} & +  6.00 y_{24} & + 10.00 y_{25} & +  5.00 y_{26} & +  2.00 y_{27} & -1.00 y_{28} & -3.00 y_{29} & -9.00 y_{30} & -2.00 y_{31}\\
 y_{7}   &  1.0 & + 10.00 y_{16} & -4.00 y_{17} & -9.00 y_{18} & +  3.00 y_{19} & -5.00 y_{20} & -6.00 y_{21} & -5.00 y_{22} & -2.00 y_{23} & + 10.00 y_{24} & -7.00 y_{25} & -3.00 y_{26} & +  2.00 y_{27} &   & -4.00 y_{29} & +  7.00 y_{30} & + 10.00 y_{31}\\
 y_{8}   &  1.0 & + 10.00 y_{16} & +  7.00 y_{17} & +  1.00 y_{18} & +  5.00 y_{19} & -8.00 y_{20} & -6.00 y_{21} &   & +  2.00 y_{23} & +  8.00 y_{24} & + 10.00 y_{25} & + 10.00 y_{26} & -6.00 y_{27} & +  5.00 y_{28} & +  5.00 y_{29} & -10.00 y_{30} & +  5.00 y_{31}\\
 y_{9}   &  1.0 & -10.00 y_{16} & -6.00 y_{17} & -4.00 y_{18} & +  2.00 y_{19} & -5.00 y_{20} & +  4.00 y_{21} & +  4.00 y_{22} & +  1.00 y_{23} & +  3.00 y_{24} & -4.00 y_{25} & +  6.00 y_{26} & -6.00 y_{27} & +  1.00 y_{28} &   & -4.00 y_{30} & +  2.00 y_{31}\\
 y_{10}   &  1.0 & +  6.00 y_{16} & -4.00 y_{17} & +  3.00 y_{18} & -3.00 y_{19} & +  3.00 y_{20} & +  4.00 y_{21} & -10.00 y_{22} & +  3.00 y_{23} & -3.00 y_{24} & -2.00 y_{25} & -1.00 y_{26} & -2.00 y_{27} & +  4.00 y_{28} & -6.00 y_{29} & +  5.00 y_{30} & -9.00 y_{31}\\
 y_{11}   &  1.0 & +  9.00 y_{16} & + 10.00 y_{17} & +  9.00 y_{18} &   & -8.00 y_{20} & -1.00 y_{21} & + 10.00 y_{22} & +  1.00 y_{23} & -9.00 y_{24} & -5.00 y_{25} & +  3.00 y_{26} & -3.00 y_{27} & +  1.00 y_{28} & -1.00 y_{29} & +  7.00 y_{30} & -4.00 y_{31}\\
 y_{12}   &  1.0 & -1.00 y_{16} & +  2.00 y_{17} & -5.00 y_{18} & +  3.00 y_{19} & +  3.00 y_{20} & + 10.00 y_{21} & -2.00 y_{22} & +  4.00 y_{23} & +  1.00 y_{24} & +  5.00 y_{25} & -7.00 y_{26} & +  8.00 y_{27} & +  2.00 y_{28} & +  7.00 y_{29} & -10.00 y_{30} & +  3.00 y_{31}\\
 y_{13}   &  1.0 & -5.00 y_{16} & +  9.00 y_{17} & +  4.00 y_{18} & -8.00 y_{19} & +  5.00 y_{20} & +  8.00 y_{21} & -1.00 y_{22} & -4.00 y_{23} & -4.00 y_{24} & -9.00 y_{25} & -7.00 y_{26} & +  9.00 y_{27} & -9.00 y_{28} & -2.00 y_{29} & +  7.00 y_{30} & +  2.00 y_{31}\\
 y_{14}   &  1.0  &   & -8.00 y_{17} & +  4.00 y_{18} & +  4.00 y_{19} & -6.00 y_{20} & -3.00 y_{21} & +  7.00 y_{22} & +  3.00 y_{23} & +  8.00 y_{24} & +  7.00 y_{25} & -6.00 y_{26} & -3.00 y_{27} & -1.00 y_{28} & -9.00 y_{29} & +  3.00 y_{30} & +  3.00 y_{31}\\
 y_{15}   &  1.0 & +  2.00 y_{16} & +  9.00 y_{17} & +  5.00 y_{18} & -2.00 y_{19} & -7.00 y_{20} & -10.00 y_{21} &   & + 10.00 y_{23} & +  9.00 y_{24} & -5.00 y_{25} & -7.00 y_{26} & -7.00 y_{27} & -5.00 y_{28} & +  4.00 y_{29} &   & -4.00 y_{31}\\
\hline
z    &  -0  &   & -57.00 y_{17} & +  1.00 y_{18} &   & + 64.00 y_{20} & + 15.00 y_{21} & -20.00 y_{22} & -107.00 y_{23} & -117.00 y_{24} & -29.00 y_{25} & +  6.00 y_{26} & +  2.00 y_{27} & -41.00 y_{28} & +  5.00 y_{29} & -4.00 y_{30} & -32.00 y_{31}\\
\end{array}\]
Initialization succeeded in finding final dual dictionary with 20 pivots
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{19}   &  0.120781306034 & -0.04 y_{3} & +  1.26 y_{17} & -0.07 y_{6} & -0.04 y_{10} & -0.00 y_{8} & -0.45 y_{21} & +  0.01 y_{7} & +  0.57 y_{23} & +  0.55 y_{24} & -0.02 y_{15} & +  0.56 y_{25} & -0.09 y_{27} & +  0.14 y_{28} & +  0.01 y_{14} & +  0.04 y_{9} & -0.58 y_{31}\\
 y_{18}   &  0.0154054834416 & +  0.02 y_{3} & -0.17 y_{17} & -0.01 y_{6} & +  0.02 y_{10} & +  0.02 y_{8} & -0.00 y_{21} & -0.06 y_{7} & -0.37 y_{23} & +  0.37 y_{24} & -0.01 y_{15} & -0.84 y_{25} & +  0.26 y_{27} & -0.30 y_{28} & +  0.03 y_{14} & -0.03 y_{9} & +  0.53 y_{31}\\
 y_{30}   &  0.099913507188 & +  0.09 y_{3} & -0.19 y_{17} & +  0.01 y_{6} & -0.04 y_{10} & -0.00 y_{8} & +  0.42 y_{21} & +  0.00 y_{7} & +  0.43 y_{23} & +  0.18 y_{24} & -0.10 y_{15} & -0.82 y_{25} & -0.79 y_{27} & -0.57 y_{28} & +  0.02 y_{14} & -0.08 y_{9} & -0.99 y_{31}\\
 y_{4}   &  0.879469702541 & +  0.42 y_{3} & -23.89 y_{17} & +  0.21 y_{6} & -0.08 y_{10} & -0.19 y_{8} & +  3.44 y_{21} & +  0.38 y_{7} & +  2.83 y_{23} & +  4.00 y_{24} & +  0.42 y_{15} & +  4.03 y_{25} & -7.07 y_{27} & -3.79 y_{28} & -0.87 y_{14} & -0.17 y_{9} & -2.13 y_{31}\\
 y_{5}   &  0.591842640785 & -0.82 y_{3} & -6.30 y_{17} & +  0.13 y_{6} & -0.19 y_{10} & -0.13 y_{8} & + 12.81 y_{21} & +  0.71 y_{7} & -12.16 y_{23} & -11.76 y_{24} & +  1.49 y_{15} & +  7.43 y_{25} & + 10.75 y_{27} & + 18.07 y_{28} & -0.99 y_{14} & +  0.21 y_{9} & + 11.87 y_{31}\\
 y_{2}   &  2.33228192891 & +  0.46 y_{3} & +  2.16 y_{17} & +  0.15 y_{6} & -1.37 y_{10} & +  0.40 y_{8} & +  7.11 y_{21} & +  0.63 y_{7} & +  4.68 y_{23} & -7.73 y_{24} & -0.96 y_{15} & -5.21 y_{25} & -16.09 y_{27} & -6.76 y_{28} & +  0.30 y_{14} & -0.95 y_{9} & -28.06 y_{31}\\
 y_{1}   &  0.428774736479 & +  0.25 y_{3} & + 15.41 y_{17} & -0.14 y_{6} & -0.02 y_{10} & -0.49 y_{8} & -9.02 y_{21} & +  0.37 y_{7} & +  8.12 y_{23} & -4.86 y_{24} & -0.03 y_{15} & + 12.06 y_{25} & -3.86 y_{27} & +  9.80 y_{28} & +  0.09 y_{14} & +  0.55 y_{9} & +  1.76 y_{31}\\
 y_{22}   &  0.103831300973 & +  0.05 y_{3} & -0.65 y_{17} & +  0.04 y_{6} & -0.08 y_{10} & +  0.02 y_{8} & +  0.58 y_{21} & -0.01 y_{7} & +  0.45 y_{23} & -0.27 y_{24} & -0.07 y_{15} & -1.67 y_{25} & -0.76 y_{27} & -0.11 y_{28} & +  0.05 y_{14} & -0.10 y_{9} & -0.97 y_{31}\\
 y_{20}   &  0.203201485557 & -0.02 y_{3} & +  0.21 y_{17} & -0.01 y_{6} & -0.02 y_{10} & -0.02 y_{8} & -0.64 y_{21} & -0.02 y_{7} & +  0.79 y_{23} & +  1.16 y_{24} & -0.05 y_{15} & -0.29 y_{25} & -0.87 y_{27} & +  0.05 y_{28} & -0.01 y_{14} & -0.05 y_{9} & +  0.07 y_{31}\\
 y_{16}   &  0.0214972072441 & +  0.01 y_{3} & -0.67 y_{17} & +  0.02 y_{6} & -0.02 y_{10} & +  0.04 y_{8} & +  0.60 y_{21} & +  0.02 y_{7} & +  0.19 y_{23} & -0.35 y_{24} & -0.02 y_{15} & -0.97 y_{25} & -0.43 y_{27} & -0.18 y_{28} & +  0.01 y_{14} & -0.08 y_{9} & -0.46 y_{31}\\
 y_{11}   &  1.31560035669 & +  1.73 y_{3} & -6.47 y_{17} & +  0.64 y_{6} & -0.64 y_{10} & +  0.92 y_{8} & + 17.11 y_{21} & -0.44 y_{7} & +  1.39 y_{23} & -19.06 y_{24} & -1.61 y_{15} & -45.64 y_{25} & -11.07 y_{27} & -11.91 y_{28} & +  1.29 y_{14} & -2.20 y_{9} & -21.55 y_{31}\\
 y_{12}   &  1.64948733115 & -1.58 y_{3} & +  5.26 y_{17} & -0.58 y_{6} & -0.32 y_{10} & -0.51 y_{8} & +  6.01 y_{21} & +  0.42 y_{7} & +  3.23 y_{23} & +  3.07 y_{24} & +  1.74 y_{15} & + 33.30 y_{25} & + 12.84 y_{27} & + 18.19 y_{28} & -0.95 y_{14} & +  1.14 y_{9} & + 11.23 y_{31}\\
 y_{13}   &  1.2655871549 & +  0.34 y_{3} & +  5.11 y_{17} & +  0.25 y_{6} & +  0.25 y_{10} & -0.52 y_{8} & +  7.70 y_{21} & -0.28 y_{7} & -7.24 y_{23} & +  0.07 y_{24} & +  0.09 y_{15} & -8.29 y_{25} & +  6.30 y_{27} & -7.60 y_{28} & +  0.03 y_{14} & -0.42 y_{9} & +  9.89 y_{31}\\
 y_{29}   &  0.146303358462 & +  0.02 y_{3} & -1.00 y_{17} & -0.01 y_{6} & -0.07 y_{10} & +  0.00 y_{8} & +  0.58 y_{21} & -0.00 y_{7} & +  0.16 y_{23} & +  0.20 y_{24} & +  0.00 y_{15} & +  0.18 y_{25} & -0.37 y_{27} & +  0.16 y_{28} & -0.05 y_{14} & -0.04 y_{9} & -0.49 y_{31}\\
 y_{26}   &  0.00589460779699 & +  0.07 y_{3} & -0.17 y_{17} & +  0.02 y_{6} & +  0.01 y_{10} & +  0.05 y_{8} & -0.16 y_{21} & -0.02 y_{7} & +  0.35 y_{23} & +  0.25 y_{24} & -0.10 y_{15} & -1.36 y_{25} & -0.25 y_{27} & -0.98 y_{28} & +  0.01 y_{14} & -0.03 y_{9} & -0.50 y_{31}\\
\hline
z    &  11.3109049499 & -1.97 y_{3} & -36.09 y_{17} & -1.36 y_{6} & -0.15 y_{10} & -1.19 y_{8} & -37.03 y_{21} & -1.22 y_{7} & -64.47 y_{23} & -34.95 y_{24} & -2.01 y_{15} & -18.78 y_{25} & -38.36 y_{27} & -38.79 y_{28} & -2.11 y_{14} & -1.30 y_{9} & -9.21 y_{31}\\
\end{array}\]
Primal Dictionary is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{3}   &  1.96761857307 & +  0.04 x_{19} & -0.02 x_{18} & -0.09 x_{30} & -0.42 x_{4} & +  0.82 x_{5} & -0.46 x_{2} & -0.25 x_{1} & -0.05 x_{22} & +  0.02 x_{20} & -0.01 x_{16} & -1.73 x_{11} & +  1.58 x_{12} & -0.34 x_{13} & -0.02 x_{29} & -0.07 x_{26}\\
 x_{17}   &  36.0864170567 & -1.26 x_{19} & +  0.17 x_{18} & +  0.19 x_{30} & + 23.89 x_{4} & +  6.30 x_{5} & -2.16 x_{2} & -15.41 x_{1} & +  0.65 x_{22} & -0.21 x_{20} & +  0.67 x_{16} & +  6.47 x_{11} & -5.26 x_{12} & -5.11 x_{13} & +  1.00 x_{29} & +  0.17 x_{26}\\
 x_{6}   &  1.35786219052 & +  0.07 x_{19} & +  0.01 x_{18} & -0.01 x_{30} & -0.21 x_{4} & -0.13 x_{5} & -0.15 x_{2} & +  0.14 x_{1} & -0.04 x_{22} & +  0.01 x_{20} & -0.02 x_{16} & -0.64 x_{11} & +  0.58 x_{12} & -0.25 x_{13} & +  0.01 x_{29} & -0.02 x_{26}\\
 x_{10}   &  0.154039915943 & +  0.04 x_{19} & -0.02 x_{18} & +  0.04 x_{30} & +  0.08 x_{4} & +  0.19 x_{5} & +  1.37 x_{2} & +  0.02 x_{1} & +  0.08 x_{22} & +  0.02 x_{20} & +  0.02 x_{16} & +  0.64 x_{11} & +  0.32 x_{12} & -0.25 x_{13} & +  0.07 x_{29} & -0.01 x_{26}\\
 x_{8}   &  1.19031322592 & +  0.00 x_{19} & -0.02 x_{18} & +  0.00 x_{30} & +  0.19 x_{4} & +  0.13 x_{5} & -0.40 x_{2} & +  0.49 x_{1} & -0.02 x_{22} & +  0.02 x_{20} & -0.04 x_{16} & -0.92 x_{11} & +  0.51 x_{12} & +  0.52 x_{13} & -0.00 x_{29} & -0.05 x_{26}\\
 x_{21}   &  37.0347249674 & +  0.45 x_{19} & +  0.00 x_{18} & -0.42 x_{30} & -3.44 x_{4} & -12.81 x_{5} & -7.11 x_{2} & +  9.02 x_{1} & -0.58 x_{22} & +  0.64 x_{20} & -0.60 x_{16} & -17.11 x_{11} & -6.01 x_{12} & -7.70 x_{13} & -0.58 x_{29} & +  0.16 x_{26}\\
 x_{7}   &  1.21912111918 & -0.01 x_{19} & +  0.06 x_{18} & -0.00 x_{30} & -0.38 x_{4} & -0.71 x_{5} & -0.63 x_{2} & -0.37 x_{1} & +  0.01 x_{22} & +  0.02 x_{20} & -0.02 x_{16} & +  0.44 x_{11} & -0.42 x_{12} & +  0.28 x_{13} & +  0.00 x_{29} & +  0.02 x_{26}\\
 x_{23}   &  64.4658706973 & -0.57 x_{19} & +  0.37 x_{18} & -0.43 x_{30} & -2.83 x_{4} & + 12.16 x_{5} & -4.68 x_{2} & -8.12 x_{1} & -0.45 x_{22} & -0.79 x_{20} & -0.19 x_{16} & -1.39 x_{11} & -3.23 x_{12} & +  7.24 x_{13} & -0.16 x_{29} & -0.35 x_{26}\\
 x_{24}   &  34.9527679472 & -0.55 x_{19} & -0.37 x_{18} & -0.18 x_{30} & -4.00 x_{4} & + 11.76 x_{5} & +  7.73 x_{2} & +  4.86 x_{1} & +  0.27 x_{22} & -1.16 x_{20} & +  0.35 x_{16} & + 19.06 x_{11} & -3.07 x_{12} & -0.07 x_{13} & -0.20 x_{29} & -0.25 x_{26}\\
 x_{15}   &  2.01225398086 & +  0.02 x_{19} & +  0.01 x_{18} & +  0.10 x_{30} & -0.42 x_{4} & -1.49 x_{5} & +  0.96 x_{2} & +  0.03 x_{1} & +  0.07 x_{22} & +  0.05 x_{20} & +  0.02 x_{16} & +  1.61 x_{11} & -1.74 x_{12} & -0.09 x_{13} & -0.00 x_{29} & +  0.10 x_{26}\\
 x_{25}   &  18.7844153343 & -0.56 x_{19} & +  0.84 x_{18} & +  0.82 x_{30} & -4.03 x_{4} & -7.43 x_{5} & +  5.21 x_{2} & -12.06 x_{1} & +  1.67 x_{22} & +  0.29 x_{20} & +  0.97 x_{16} & + 45.64 x_{11} & -33.30 x_{12} & +  8.29 x_{13} & -0.18 x_{29} & +  1.36 x_{26}\\
 x_{27}   &  38.3565841746 & +  0.09 x_{19} & -0.26 x_{18} & +  0.79 x_{30} & +  7.07 x_{4} & -10.75 x_{5} & + 16.09 x_{2} & +  3.86 x_{1} & +  0.76 x_{22} & +  0.87 x_{20} & +  0.43 x_{16} & + 11.07 x_{11} & -12.84 x_{12} & -6.30 x_{13} & +  0.37 x_{29} & +  0.25 x_{26}\\
 x_{28}   &  38.7855392591 & -0.14 x_{19} & +  0.30 x_{18} & +  0.57 x_{30} & +  3.79 x_{4} & -18.07 x_{5} & +  6.76 x_{2} & -9.80 x_{1} & +  0.11 x_{22} & -0.05 x_{20} & +  0.18 x_{16} & + 11.91 x_{11} & -18.19 x_{12} & +  7.60 x_{13} & -0.16 x_{29} & +  0.98 x_{26}\\
 x_{14}   &  2.10715159716 & -0.01 x_{19} & -0.03 x_{18} & -0.02 x_{30} & +  0.87 x_{4} & +  0.99 x_{5} & -0.30 x_{2} & -0.09 x_{1} & -0.05 x_{22} & +  0.01 x_{20} & -0.01 x_{16} & -1.29 x_{11} & +  0.95 x_{12} & -0.03 x_{13} & +  0.05 x_{29} & -0.01 x_{26}\\
 x_{9}   &  1.30254434729 & -0.04 x_{19} & +  0.03 x_{18} & +  0.08 x_{30} & +  0.17 x_{4} & -0.21 x_{5} & +  0.95 x_{2} & -0.55 x_{1} & +  0.10 x_{22} & +  0.05 x_{20} & +  0.08 x_{16} & +  2.20 x_{11} & -1.14 x_{12} & +  0.42 x_{13} & +  0.04 x_{29} & +  0.03 x_{26}\\
 x_{31}   &  9.21130444827 & +  0.58 x_{19} & -0.53 x_{18} & +  0.99 x_{30} & +  2.13 x_{4} & -11.87 x_{5} & + 28.06 x_{2} & -1.76 x_{1} & +  0.97 x_{22} & -0.07 x_{20} & +  0.46 x_{16} & + 21.55 x_{11} & -11.23 x_{12} & -9.89 x_{13} & +  0.49 x_{29} & +  0.50 x_{26}\\
\hline
z    &  -11.3109049499 & -0.12 x_{19} & -0.02 x_{18} & -0.10 x_{30} & -0.88 x_{4} & -0.59 x_{5} & -2.33 x_{2} & -0.43 x_{1} & -0.10 x_{22} & -0.20 x_{20} & -0.02 x_{16} & -1.32 x_{11} & -1.65 x_{12} & -1.27 x_{13} & -0.15 x_{29} & -0.01 x_{26}\\
\end{array}\]
Primal Dictionary with original objective is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{3}   &  1.96761857307 & +  0.04 x_{19} & -0.02 x_{18} & -0.09 x_{30} & -0.42 x_{4} & +  0.82 x_{5} & -0.46 x_{2} & -0.25 x_{1} & -0.05 x_{22} & +  0.02 x_{20} & -0.01 x_{16} & -1.73 x_{11} & +  1.58 x_{12} & -0.34 x_{13} & -0.02 x_{29} & -0.07 x_{26}\\
 x_{17}   &  36.0864170567 & -1.26 x_{19} & +  0.17 x_{18} & +  0.19 x_{30} & + 23.89 x_{4} & +  6.30 x_{5} & -2.16 x_{2} & -15.41 x_{1} & +  0.65 x_{22} & -0.21 x_{20} & +  0.67 x_{16} & +  6.47 x_{11} & -5.26 x_{12} & -5.11 x_{13} & +  1.00 x_{29} & +  0.17 x_{26}\\
 x_{6}   &  1.35786219052 & +  0.07 x_{19} & +  0.01 x_{18} & -0.01 x_{30} & -0.21 x_{4} & -0.13 x_{5} & -0.15 x_{2} & +  0.14 x_{1} & -0.04 x_{22} & +  0.01 x_{20} & -0.02 x_{16} & -0.64 x_{11} & +  0.58 x_{12} & -0.25 x_{13} & +  0.01 x_{29} & -0.02 x_{26}\\
 x_{10}   &  0.154039915943 & +  0.04 x_{19} & -0.02 x_{18} & +  0.04 x_{30} & +  0.08 x_{4} & +  0.19 x_{5} & +  1.37 x_{2} & +  0.02 x_{1} & +  0.08 x_{22} & +  0.02 x_{20} & +  0.02 x_{16} & +  0.64 x_{11} & +  0.32 x_{12} & -0.25 x_{13} & +  0.07 x_{29} & -0.01 x_{26}\\
 x_{8}   &  1.19031322592 & +  0.00 x_{19} & -0.02 x_{18} & +  0.00 x_{30} & +  0.19 x_{4} & +  0.13 x_{5} & -0.40 x_{2} & +  0.49 x_{1} & -0.02 x_{22} & +  0.02 x_{20} & -0.04 x_{16} & -0.92 x_{11} & +  0.51 x_{12} & +  0.52 x_{13} & -0.00 x_{29} & -0.05 x_{26}\\
 x_{21}   &  37.0347249674 & +  0.45 x_{19} & +  0.00 x_{18} & -0.42 x_{30} & -3.44 x_{4} & -12.81 x_{5} & -7.11 x_{2} & +  9.02 x_{1} & -0.58 x_{22} & +  0.64 x_{20} & -0.60 x_{16} & -17.11 x_{11} & -6.01 x_{12} & -7.70 x_{13} & -0.58 x_{29} & +  0.16 x_{26}\\
 x_{7}   &  1.21912111918 & -0.01 x_{19} & +  0.06 x_{18} & -0.00 x_{30} & -0.38 x_{4} & -0.71 x_{5} & -0.63 x_{2} & -0.37 x_{1} & +  0.01 x_{22} & +  0.02 x_{20} & -0.02 x_{16} & +  0.44 x_{11} & -0.42 x_{12} & +  0.28 x_{13} & +  0.00 x_{29} & +  0.02 x_{26}\\
 x_{23}   &  64.4658706973 & -0.57 x_{19} & +  0.37 x_{18} & -0.43 x_{30} & -2.83 x_{4} & + 12.16 x_{5} & -4.68 x_{2} & -8.12 x_{1} & -0.45 x_{22} & -0.79 x_{20} & -0.19 x_{16} & -1.39 x_{11} & -3.23 x_{12} & +  7.24 x_{13} & -0.16 x_{29} & -0.35 x_{26}\\
 x_{24}   &  34.9527679472 & -0.55 x_{19} & -0.37 x_{18} & -0.18 x_{30} & -4.00 x_{4} & + 11.76 x_{5} & +  7.73 x_{2} & +  4.86 x_{1} & +  0.27 x_{22} & -1.16 x_{20} & +  0.35 x_{16} & + 19.06 x_{11} & -3.07 x_{12} & -0.07 x_{13} & -0.20 x_{29} & -0.25 x_{26}\\
 x_{15}   &  2.01225398086 & +  0.02 x_{19} & +  0.01 x_{18} & +  0.10 x_{30} & -0.42 x_{4} & -1.49 x_{5} & +  0.96 x_{2} & +  0.03 x_{1} & +  0.07 x_{22} & +  0.05 x_{20} & +  0.02 x_{16} & +  1.61 x_{11} & -1.74 x_{12} & -0.09 x_{13} & -0.00 x_{29} & +  0.10 x_{26}\\
 x_{25}   &  18.7844153343 & -0.56 x_{19} & +  0.84 x_{18} & +  0.82 x_{30} & -4.03 x_{4} & -7.43 x_{5} & +  5.21 x_{2} & -12.06 x_{1} & +  1.67 x_{22} & +  0.29 x_{20} & +  0.97 x_{16} & + 45.64 x_{11} & -33.30 x_{12} & +  8.29 x_{13} & -0.18 x_{29} & +  1.36 x_{26}\\
 x_{27}   &  38.3565841746 & +  0.09 x_{19} & -0.26 x_{18} & +  0.79 x_{30} & +  7.07 x_{4} & -10.75 x_{5} & + 16.09 x_{2} & +  3.86 x_{1} & +  0.76 x_{22} & +  0.87 x_{20} & +  0.43 x_{16} & + 11.07 x_{11} & -12.84 x_{12} & -6.30 x_{13} & +  0.37 x_{29} & +  0.25 x_{26}\\
 x_{28}   &  38.7855392591 & -0.14 x_{19} & +  0.30 x_{18} & +  0.57 x_{30} & +  3.79 x_{4} & -18.07 x_{5} & +  6.76 x_{2} & -9.80 x_{1} & +  0.11 x_{22} & -0.05 x_{20} & +  0.18 x_{16} & + 11.91 x_{11} & -18.19 x_{12} & +  7.60 x_{13} & -0.16 x_{29} & +  0.98 x_{26}\\
 x_{14}   &  2.10715159716 & -0.01 x_{19} & -0.03 x_{18} & -0.02 x_{30} & +  0.87 x_{4} & +  0.99 x_{5} & -0.30 x_{2} & -0.09 x_{1} & -0.05 x_{22} & +  0.01 x_{20} & -0.01 x_{16} & -1.29 x_{11} & +  0.95 x_{12} & -0.03 x_{13} & +  0.05 x_{29} & -0.01 x_{26}\\
 x_{9}   &  1.30254434729 & -0.04 x_{19} & +  0.03 x_{18} & +  0.08 x_{30} & +  0.17 x_{4} & -0.21 x_{5} & +  0.95 x_{2} & -0.55 x_{1} & +  0.10 x_{22} & +  0.05 x_{20} & +  0.08 x_{16} & +  2.20 x_{11} & -1.14 x_{12} & +  0.42 x_{13} & +  0.04 x_{29} & +  0.03 x_{26}\\
 x_{31}   &  9.21130444827 & +  0.58 x_{19} & -0.53 x_{18} & +  0.99 x_{30} & +  2.13 x_{4} & -11.87 x_{5} & + 28.06 x_{2} & -1.76 x_{1} & +  0.97 x_{22} & -0.07 x_{20} & +  0.46 x_{16} & + 21.55 x_{11} & -11.23 x_{12} & -9.89 x_{13} & +  0.49 x_{29} & +  0.50 x_{26}\\
\hline
z    &  -12.4968552589 & -0.28 x_{19} & +  0.18 x_{18} & -0.13 x_{30} & -0.49 x_{4} & -6.67 x_{5} & -5.63 x_{2} & -4.64 x_{1} & -0.16 x_{22} & -0.25 x_{20} & -0.06 x_{16} & -2.63 x_{11} & -6.50 x_{12} & -2.64 x_{13} & -0.54 x_{29} & +  0.42 x_{26}\\
\end{array}\]
\section{Optimization Phase Simplex}
Starting Dictionary is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{3}   &  1.96761857307 & +  0.04 x_{19} & -0.02 x_{18} & -0.09 x_{30} & -0.42 x_{4} & +  0.82 x_{5} & -0.46 x_{2} & -0.25 x_{1} & -0.05 x_{22} & +  0.02 x_{20} & -0.01 x_{16} & -1.73 x_{11} & +  1.58 x_{12} & -0.34 x_{13} & -0.02 x_{29} & -0.07 x_{26}\\
 x_{17}   &  36.0864170567 & -1.26 x_{19} & +  0.17 x_{18} & +  0.19 x_{30} & + 23.89 x_{4} & +  6.30 x_{5} & -2.16 x_{2} & -15.41 x_{1} & +  0.65 x_{22} & -0.21 x_{20} & +  0.67 x_{16} & +  6.47 x_{11} & -5.26 x_{12} & -5.11 x_{13} & +  1.00 x_{29} & +  0.17 x_{26}\\
 x_{6}   &  1.35786219052 & +  0.07 x_{19} & +  0.01 x_{18} & -0.01 x_{30} & -0.21 x_{4} & -0.13 x_{5} & -0.15 x_{2} & +  0.14 x_{1} & -0.04 x_{22} & +  0.01 x_{20} & -0.02 x_{16} & -0.64 x_{11} & +  0.58 x_{12} & -0.25 x_{13} & +  0.01 x_{29} & -0.02 x_{26}\\
 x_{10}   &  0.154039915943 & +  0.04 x_{19} & -0.02 x_{18} & +  0.04 x_{30} & +  0.08 x_{4} & +  0.19 x_{5} & +  1.37 x_{2} & +  0.02 x_{1} & +  0.08 x_{22} & +  0.02 x_{20} & +  0.02 x_{16} & +  0.64 x_{11} & +  0.32 x_{12} & -0.25 x_{13} & +  0.07 x_{29} & -0.01 x_{26}\\
 x_{8}   &  1.19031322592 & +  0.00 x_{19} & -0.02 x_{18} & +  0.00 x_{30} & +  0.19 x_{4} & +  0.13 x_{5} & -0.40 x_{2} & +  0.49 x_{1} & -0.02 x_{22} & +  0.02 x_{20} & -0.04 x_{16} & -0.92 x_{11} & +  0.51 x_{12} & +  0.52 x_{13} & -0.00 x_{29} & -0.05 x_{26}\\
 x_{21}   &  37.0347249674 & +  0.45 x_{19} & +  0.00 x_{18} & -0.42 x_{30} & -3.44 x_{4} & -12.81 x_{5} & -7.11 x_{2} & +  9.02 x_{1} & -0.58 x_{22} & +  0.64 x_{20} & -0.60 x_{16} & -17.11 x_{11} & -6.01 x_{12} & -7.70 x_{13} & -0.58 x_{29} & +  0.16 x_{26}\\
 x_{7}   &  1.21912111918 & -0.01 x_{19} & +  0.06 x_{18} & -0.00 x_{30} & -0.38 x_{4} & -0.71 x_{5} & -0.63 x_{2} & -0.37 x_{1} & +  0.01 x_{22} & +  0.02 x_{20} & -0.02 x_{16} & +  0.44 x_{11} & -0.42 x_{12} & +  0.28 x_{13} & +  0.00 x_{29} & +  0.02 x_{26}\\
 x_{23}   &  64.4658706973 & -0.57 x_{19} & +  0.37 x_{18} & -0.43 x_{30} & -2.83 x_{4} & + 12.16 x_{5} & -4.68 x_{2} & -8.12 x_{1} & -0.45 x_{22} & -0.79 x_{20} & -0.19 x_{16} & -1.39 x_{11} & -3.23 x_{12} & +  7.24 x_{13} & -0.16 x_{29} & -0.35 x_{26}\\
 x_{24}   &  34.9527679472 & -0.55 x_{19} & -0.37 x_{18} & -0.18 x_{30} & -4.00 x_{4} & + 11.76 x_{5} & +  7.73 x_{2} & +  4.86 x_{1} & +  0.27 x_{22} & -1.16 x_{20} & +  0.35 x_{16} & + 19.06 x_{11} & -3.07 x_{12} & -0.07 x_{13} & -0.20 x_{29} & -0.25 x_{26}\\
 x_{15}   &  2.01225398086 & +  0.02 x_{19} & +  0.01 x_{18} & +  0.10 x_{30} & -0.42 x_{4} & -1.49 x_{5} & +  0.96 x_{2} & +  0.03 x_{1} & +  0.07 x_{22} & +  0.05 x_{20} & +  0.02 x_{16} & +  1.61 x_{11} & -1.74 x_{12} & -0.09 x_{13} & -0.00 x_{29} & +  0.10 x_{26}\\
 x_{25}   &  18.7844153343 & -0.56 x_{19} & +  0.84 x_{18} & +  0.82 x_{30} & -4.03 x_{4} & -7.43 x_{5} & +  5.21 x_{2} & -12.06 x_{1} & +  1.67 x_{22} & +  0.29 x_{20} & +  0.97 x_{16} & + 45.64 x_{11} & -33.30 x_{12} & +  8.29 x_{13} & -0.18 x_{29} & +  1.36 x_{26}\\
 x_{27}   &  38.3565841746 & +  0.09 x_{19} & -0.26 x_{18} & +  0.79 x_{30} & +  7.07 x_{4} & -10.75 x_{5} & + 16.09 x_{2} & +  3.86 x_{1} & +  0.76 x_{22} & +  0.87 x_{20} & +  0.43 x_{16} & + 11.07 x_{11} & -12.84 x_{12} & -6.30 x_{13} & +  0.37 x_{29} & +  0.25 x_{26}\\
 x_{28}   &  38.7855392591 & -0.14 x_{19} & +  0.30 x_{18} & +  0.57 x_{30} & +  3.79 x_{4} & -18.07 x_{5} & +  6.76 x_{2} & -9.80 x_{1} & +  0.11 x_{22} & -0.05 x_{20} & +  0.18 x_{16} & + 11.91 x_{11} & -18.19 x_{12} & +  7.60 x_{13} & -0.16 x_{29} & +  0.98 x_{26}\\
 x_{14}   &  2.10715159716 & -0.01 x_{19} & -0.03 x_{18} & -0.02 x_{30} & +  0.87 x_{4} & +  0.99 x_{5} & -0.30 x_{2} & -0.09 x_{1} & -0.05 x_{22} & +  0.01 x_{20} & -0.01 x_{16} & -1.29 x_{11} & +  0.95 x_{12} & -0.03 x_{13} & +  0.05 x_{29} & -0.01 x_{26}\\
 x_{9}   &  1.30254434729 & -0.04 x_{19} & +  0.03 x_{18} & +  0.08 x_{30} & +  0.17 x_{4} & -0.21 x_{5} & +  0.95 x_{2} & -0.55 x_{1} & +  0.10 x_{22} & +  0.05 x_{20} & +  0.08 x_{16} & +  2.20 x_{11} & -1.14 x_{12} & +  0.42 x_{13} & +  0.04 x_{29} & +  0.03 x_{26}\\
 x_{31}   &  9.21130444827 & +  0.58 x_{19} & -0.53 x_{18} & +  0.99 x_{30} & +  2.13 x_{4} & -11.87 x_{5} & + 28.06 x_{2} & -1.76 x_{1} & +  0.97 x_{22} & -0.07 x_{20} & +  0.46 x_{16} & + 21.55 x_{11} & -11.23 x_{12} & -9.89 x_{13} & +  0.49 x_{29} & +  0.50 x_{26}\\
\hline
z    &  -12.4968552589 & -0.28 x_{19} & +  0.18 x_{18} & -0.13 x_{30} & -0.49 x_{4} & -6.67 x_{5} & -5.63 x_{2} & -4.64 x_{1} & -0.16 x_{22} & -0.25 x_{20} & -0.06 x_{16} & -2.63 x_{11} & -6.50 x_{12} & -2.64 x_{13} & -0.54 x_{29} & +  0.42 x_{26}\\
\end{array}\]


 $ x_{18} $ enters and $ x_{10} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{3}   &  1.82599025447 & +  0.01 x_{19} & +  0.92 x_{10} & -0.12 x_{30} & -0.49 x_{4} & +  0.65 x_{5} & -1.72 x_{2} & -0.27 x_{1} & -0.12 x_{22} & -0.00 x_{20} & -0.03 x_{16} & -2.33 x_{11} & +  1.29 x_{12} & -0.11 x_{13} & -0.09 x_{29} & -0.06 x_{26}\\
 x_{17}   &  37.1611639928 & -0.99 x_{19} & -6.98 x_{10} & +  0.44 x_{30} & + 24.43 x_{4} & +  7.62 x_{5} & +  7.41 x_{2} & -15.24 x_{1} & +  1.18 x_{22} & -0.04 x_{20} & +  0.77 x_{16} & + 10.96 x_{11} & -3.03 x_{12} & -6.84 x_{13} & +  1.47 x_{29} & +  0.10 x_{26}\\
 x_{6}   &  1.42774775596 & +  0.09 x_{19} & -0.45 x_{10} & +  0.01 x_{30} & -0.18 x_{4} & -0.04 x_{5} & +  0.47 x_{2} & +  0.15 x_{1} & -0.00 x_{22} & +  0.02 x_{20} & -0.01 x_{16} & -0.34 x_{11} & +  0.72 x_{12} & -0.36 x_{13} & +  0.04 x_{29} & -0.03 x_{26}\\
 x_{18}   &  6.34126600747 & +  1.61 x_{19} & -41.17 x_{10} & +  1.52 x_{30} & +  3.22 x_{4} & +  7.80 x_{5} & + 56.45 x_{2} & +  1.00 x_{1} & +  3.13 x_{22} & +  1.01 x_{20} & +  0.62 x_{16} & + 26.49 x_{11} & + 13.14 x_{12} & -10.21 x_{13} & +  2.80 x_{29} & -0.40 x_{26}\\
 x_{8}   &  1.05547955433 & -0.03 x_{19} & +  0.88 x_{10} & -0.03 x_{30} & +  0.12 x_{4} & -0.03 x_{5} & -1.61 x_{2} & +  0.47 x_{1} & -0.08 x_{22} & -0.00 x_{20} & -0.05 x_{16} & -1.49 x_{11} & +  0.23 x_{12} & +  0.74 x_{13} & -0.06 x_{29} & -0.04 x_{26}\\
 x_{21}   &  37.0354243866 & +  0.45 x_{19} & -0.00 x_{10} & -0.42 x_{30} & -3.44 x_{4} & -12.81 x_{5} & -7.11 x_{2} & +  9.02 x_{1} & -0.58 x_{22} & +  0.64 x_{20} & -0.60 x_{16} & -17.11 x_{11} & -6.00 x_{12} & -7.70 x_{13} & -0.58 x_{29} & +  0.16 x_{26}\\
 x_{7}   &  1.61173385006 & +  0.09 x_{19} & -2.55 x_{10} & +  0.09 x_{30} & -0.18 x_{4} & -0.23 x_{5} & +  2.86 x_{2} & -0.31 x_{1} & +  0.21 x_{22} & +  0.08 x_{20} & +  0.02 x_{16} & +  2.08 x_{11} & +  0.40 x_{12} & -0.35 x_{13} & +  0.18 x_{29} & +  0.00 x_{26}\\
 x_{23}   &  66.8098280569 & +  0.02 x_{19} & -15.22 x_{10} & +  0.14 x_{30} & -1.64 x_{4} & + 15.04 x_{5} & + 16.19 x_{2} & -7.75 x_{1} & +  0.70 x_{22} & -0.42 x_{20} & +  0.04 x_{16} & +  8.40 x_{11} & +  1.63 x_{12} & +  3.47 x_{13} & +  0.88 x_{29} & -0.50 x_{26}\\
 x_{24}   &  32.590099564 & -1.14 x_{19} & + 15.34 x_{10} & -0.75 x_{30} & -5.20 x_{4} & +  8.85 x_{5} & -13.31 x_{2} & +  4.48 x_{1} & -0.89 x_{22} & -1.54 x_{20} & +  0.12 x_{16} & +  9.19 x_{11} & -7.96 x_{12} & +  3.74 x_{13} & -1.25 x_{29} & -0.10 x_{26}\\
 x_{15}   &  2.09392608212 & +  0.04 x_{19} & -0.53 x_{10} & +  0.12 x_{30} & -0.38 x_{4} & -1.39 x_{5} & +  1.69 x_{2} & +  0.04 x_{1} & +  0.11 x_{22} & +  0.06 x_{20} & +  0.03 x_{16} & +  1.95 x_{11} & -1.57 x_{12} & -0.22 x_{13} & +  0.03 x_{29} & +  0.10 x_{26}\\
 x_{25}   &  24.129933491 & +  0.80 x_{19} & -34.70 x_{10} & +  2.10 x_{30} & -1.32 x_{4} & -0.85 x_{5} & + 52.80 x_{2} & -11.22 x_{1} & +  4.30 x_{22} & +  1.13 x_{20} & +  1.49 x_{16} & + 67.97 x_{11} & -22.22 x_{12} & -0.31 x_{13} & +  2.18 x_{29} & +  1.03 x_{26}\\
 x_{27}   &  36.7193627219 & -0.32 x_{19} & + 10.63 x_{10} & +  0.39 x_{30} & +  6.24 x_{4} & -12.76 x_{5} & +  1.51 x_{2} & +  3.60 x_{1} & -0.05 x_{22} & +  0.61 x_{20} & +  0.27 x_{16} & +  4.23 x_{11} & -16.23 x_{12} & -3.66 x_{13} & -0.36 x_{29} & +  0.35 x_{26}\\
 x_{28}   &  40.7118293677 & +  0.34 x_{19} & -12.51 x_{10} & +  1.03 x_{30} & +  4.77 x_{4} & -15.70 x_{5} & + 23.90 x_{2} & -9.50 x_{1} & +  1.06 x_{22} & +  0.26 x_{20} & +  0.37 x_{16} & + 19.96 x_{11} & -14.20 x_{12} & +  4.50 x_{13} & +  0.69 x_{29} & +  0.86 x_{26}\\
 x_{14}   &  1.89476385604 & -0.06 x_{19} & +  1.38 x_{10} & -0.08 x_{30} & +  0.77 x_{4} & +  0.73 x_{5} & -2.19 x_{2} & -0.12 x_{1} & -0.15 x_{22} & -0.02 x_{20} & -0.03 x_{16} & -2.17 x_{11} & +  0.51 x_{12} & +  0.31 x_{13} & -0.05 x_{29} & -0.00 x_{26}\\
 x_{9}   &  1.49895386544 & +  0.01 x_{19} & -1.28 x_{10} & +  0.13 x_{30} & +  0.27 x_{4} & +  0.03 x_{5} & +  2.70 x_{2} & -0.51 x_{1} & +  0.19 x_{22} & +  0.08 x_{20} & +  0.10 x_{16} & +  3.02 x_{11} & -0.73 x_{12} & +  0.10 x_{13} & +  0.13 x_{29} & +  0.02 x_{26}\\
 x_{31}   &  5.85030325136 & -0.27 x_{19} & + 21.82 x_{10} & +  0.18 x_{30} & +  0.42 x_{4} & -16.01 x_{5} & -1.86 x_{2} & -2.29 x_{1} & -0.68 x_{22} & -0.60 x_{20} & +  0.13 x_{16} & +  7.52 x_{11} & -18.20 x_{12} & -4.48 x_{13} & -1.00 x_{29} & +  0.71 x_{26}\\
\hline
z    &  -11.3642329809 & +  0.01 x_{19} & -7.35 x_{10} & +  0.14 x_{30} & +  0.08 x_{4} & -5.28 x_{5} & +  4.45 x_{2} & -4.46 x_{1} & +  0.40 x_{22} & -0.07 x_{20} & +  0.05 x_{16} & +  2.11 x_{11} & -4.15 x_{12} & -4.46 x_{13} & -0.04 x_{29} & +  0.35 x_{26}\\
\end{array}\]


 $ x_{2} $ enters and $ x_{8} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{3}   &  0.696120683993 & +  0.04 x_{19} & -0.02 x_{10} & -0.09 x_{30} & -0.62 x_{4} & +  0.68 x_{5} & +  1.07 x_{8} & -0.78 x_{1} & -0.03 x_{22} & -0.00 x_{20} & +  0.02 x_{16} & -0.73 x_{11} & +  1.04 x_{12} & -0.90 x_{13} & -0.02 x_{29} & -0.02 x_{26}\\
 x_{17}   &  42.0352337357 & -1.13 x_{19} & -2.93 x_{10} & +  0.31 x_{30} & + 24.99 x_{4} & +  7.48 x_{5} & -4.62 x_{8} & -13.08 x_{1} & +  0.80 x_{22} & -0.05 x_{20} & +  0.55 x_{16} & +  4.09 x_{11} & -1.95 x_{12} & -3.44 x_{13} & +  1.19 x_{29} & -0.07 x_{26}\\
 x_{6}   &  1.73833746541 & +  0.08 x_{19} & -0.20 x_{10} & +  0.00 x_{30} & -0.14 x_{4} & -0.05 x_{5} & -0.29 x_{8} & +  0.29 x_{1} & -0.02 x_{22} & +  0.02 x_{20} & -0.03 x_{16} & -0.78 x_{11} & +  0.79 x_{12} & -0.15 x_{13} & +  0.03 x_{29} & -0.04 x_{26}\\
 x_{18}   &  43.4611791823 & +  0.51 x_{19} & -10.38 x_{10} & +  0.50 x_{30} & +  7.43 x_{4} & +  6.67 x_{5} & -35.17 x_{8} & + 17.49 x_{1} & +  0.24 x_{22} & +  0.91 x_{20} & -1.08 x_{16} & -25.83 x_{11} & + 21.35 x_{12} & + 15.68 x_{13} & +  0.66 x_{29} & -1.70 x_{26}\\
 x_{2}   &  0.657534264084 & -0.02 x_{19} & +  0.55 x_{10} & -0.02 x_{30} & +  0.07 x_{4} & -0.02 x_{5} & -0.62 x_{8} & +  0.29 x_{1} & -0.05 x_{22} & -0.00 x_{20} & -0.03 x_{16} & -0.93 x_{11} & +  0.15 x_{12} & +  0.46 x_{13} & -0.04 x_{29} & -0.02 x_{26}\\
 x_{21}   &  32.3627516572 & +  0.59 x_{19} & -3.88 x_{10} & -0.29 x_{30} & -3.97 x_{4} & -12.67 x_{5} & +  4.43 x_{8} & +  6.94 x_{1} & -0.21 x_{22} & +  0.65 x_{20} & -0.38 x_{16} & -10.52 x_{11} & -7.04 x_{12} & -10.96 x_{13} & -0.31 x_{29} & +  0.32 x_{26}\\
 x_{7}   &  3.49434665245 & +  0.03 x_{19} & -0.99 x_{10} & +  0.04 x_{30} & +  0.04 x_{4} & -0.29 x_{5} & -1.78 x_{8} & +  0.53 x_{1} & +  0.06 x_{22} & +  0.08 x_{20} & -0.06 x_{16} & -0.57 x_{11} & +  0.81 x_{12} & +  0.96 x_{13} & +  0.07 x_{29} & -0.07 x_{26}\\
 x_{23}   &  77.4534174259 & -0.30 x_{19} & -6.39 x_{10} & -0.16 x_{30} & -0.43 x_{4} & + 14.72 x_{5} & -10.08 x_{8} & -3.02 x_{1} & -0.12 x_{22} & -0.45 x_{20} & -0.44 x_{16} & -6.61 x_{11} & +  3.98 x_{12} & + 10.89 x_{13} & +  0.27 x_{29} & -0.87 x_{26}\\
 x_{24}   &  23.8406859172 & -0.89 x_{19} & +  8.08 x_{10} & -0.50 x_{30} & -6.20 x_{4} & +  9.12 x_{5} & +  8.29 x_{8} & +  0.60 x_{1} & -0.21 x_{22} & -1.51 x_{20} & +  0.52 x_{16} & + 21.52 x_{11} & -9.90 x_{12} & -2.37 x_{13} & -0.74 x_{29} & +  0.21 x_{26}\\
 x_{15}   &  3.20200125755 & +  0.01 x_{19} & +  0.39 x_{10} & +  0.09 x_{30} & -0.25 x_{4} & -1.42 x_{5} & -1.05 x_{8} & +  0.53 x_{1} & +  0.02 x_{22} & +  0.06 x_{20} & -0.02 x_{16} & +  0.39 x_{11} & -1.32 x_{12} & +  0.56 x_{13} & -0.03 x_{29} & +  0.06 x_{26}\\
 x_{25}   &  58.8447949445 & -0.23 x_{19} & -5.91 x_{10} & +  1.14 x_{30} & +  2.63 x_{4} & -1.91 x_{5} & -32.89 x_{8} & +  4.20 x_{1} & +  1.60 x_{22} & +  1.04 x_{20} & -0.10 x_{16} & + 19.04 x_{11} & -14.54 x_{12} & + 23.90 x_{13} & +  0.18 x_{29} & -0.19 x_{26}\\
 x_{27}   &  37.7146068688 & -0.35 x_{19} & + 11.45 x_{10} & +  0.36 x_{30} & +  6.35 x_{4} & -12.79 x_{5} & -0.94 x_{8} & +  4.04 x_{1} & -0.12 x_{22} & +  0.61 x_{20} & +  0.22 x_{16} & +  2.83 x_{11} & -16.01 x_{12} & -2.97 x_{13} & -0.42 x_{29} & +  0.32 x_{26}\\
 x_{28}   &  56.4300524502 & -0.12 x_{19} & +  0.53 x_{10} & +  0.60 x_{30} & +  6.55 x_{4} & -16.18 x_{5} & -14.89 x_{8} & -2.51 x_{1} & -0.16 x_{22} & +  0.22 x_{20} & -0.35 x_{16} & -2.19 x_{11} & -10.72 x_{12} & + 15.47 x_{13} & -0.22 x_{29} & +  0.31 x_{26}\\
 x_{14}   &  0.452090248489 & -0.02 x_{19} & +  0.18 x_{10} & -0.04 x_{30} & +  0.60 x_{4} & +  0.77 x_{5} & +  1.37 x_{8} & -0.76 x_{1} & -0.04 x_{22} & -0.02 x_{20} & +  0.03 x_{16} & -0.14 x_{11} & +  0.19 x_{12} & -0.70 x_{13} & +  0.03 x_{29} & +  0.05 x_{26}\\
 x_{9}   &  3.27357013597 & -0.04 x_{19} & +  0.20 x_{10} & +  0.08 x_{30} & +  0.47 x_{4} & -0.03 x_{5} & -1.68 x_{8} & +  0.27 x_{1} & +  0.05 x_{22} & +  0.07 x_{20} & +  0.02 x_{16} & +  0.52 x_{11} & -0.34 x_{12} & +  1.34 x_{13} & +  0.03 x_{29} & -0.04 x_{26}\\
 x_{31}   &  4.62592247546 & -0.24 x_{19} & + 20.80 x_{10} & +  0.22 x_{30} & +  0.29 x_{4} & -15.97 x_{5} & +  1.16 x_{8} & -2.83 x_{1} & -0.59 x_{22} & -0.60 x_{20} & +  0.18 x_{16} & +  9.24 x_{11} & -18.47 x_{12} & -5.33 x_{13} & -0.93 x_{29} & +  0.76 x_{26}\\
\hline
z    &  -8.43742586308 & -0.08 x_{19} & -4.93 x_{10} & +  0.06 x_{30} & +  0.41 x_{4} & -5.37 x_{5} & -2.77 x_{8} & -3.16 x_{1} & +  0.17 x_{22} & -0.08 x_{20} & -0.08 x_{16} & -2.02 x_{11} & -3.50 x_{12} & -2.42 x_{13} & -0.21 x_{29} & +  0.24 x_{26}\\
\end{array}\]


 $ x_{4} $ enters and $ x_{3} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{4}   &  1.13098246961 & +  0.07 x_{19} & -0.03 x_{10} & -0.15 x_{30} & -1.62 x_{3} & +  1.11 x_{5} & +  1.74 x_{8} & -1.26 x_{1} & -0.05 x_{22} & -0.00 x_{20} & +  0.04 x_{16} & -1.19 x_{11} & +  1.69 x_{12} & -1.46 x_{13} & -0.03 x_{29} & -0.03 x_{26}\\
 x_{17}   &  70.2951803719 & +  0.57 x_{19} & -3.65 x_{10} & -3.38 x_{30} & -40.60 x_{3} & + 35.11 x_{5} & + 38.84 x_{8} & -44.58 x_{1} & -0.33 x_{22} & -0.06 x_{20} & +  1.49 x_{16} & -25.71 x_{11} & + 40.20 x_{12} & -39.82 x_{13} & +  0.32 x_{29} & -0.78 x_{26}\\
 x_{6}   &  1.57666969234 & +  0.07 x_{19} & -0.19 x_{10} & +  0.02 x_{30} & +  0.23 x_{3} & -0.21 x_{5} & -0.54 x_{8} & +  0.47 x_{1} & -0.02 x_{22} & +  0.02 x_{20} & -0.03 x_{16} & -0.61 x_{11} & +  0.55 x_{12} & +  0.06 x_{13} & +  0.03 x_{29} & -0.03 x_{26}\\
 x_{18}   &  51.867895592 & +  1.02 x_{19} & -10.59 x_{10} & -0.60 x_{30} & -12.08 x_{3} & + 14.89 x_{5} & -22.24 x_{8} & +  8.12 x_{1} & -0.10 x_{22} & +  0.91 x_{20} & -0.80 x_{16} & -34.70 x_{11} & + 33.89 x_{12} & +  4.86 x_{13} & +  0.40 x_{29} & -1.91 x_{26}\\
 x_{2}   &  0.741976150532 & -0.01 x_{19} & +  0.54 x_{10} & -0.03 x_{30} & -0.12 x_{3} & +  0.06 x_{5} & -0.49 x_{8} & +  0.20 x_{1} & -0.05 x_{22} & -0.00 x_{20} & -0.03 x_{16} & -1.02 x_{11} & +  0.27 x_{12} & +  0.35 x_{13} & -0.04 x_{29} & -0.03 x_{26}\\
 x_{21}   &  27.87286177 & +  0.32 x_{19} & -3.77 x_{10} & +  0.30 x_{30} & +  6.45 x_{3} & -17.06 x_{5} & -2.48 x_{8} & + 11.95 x_{1} & -0.03 x_{22} & +  0.65 x_{20} & -0.53 x_{16} & -5.79 x_{11} & -13.73 x_{12} & -5.18 x_{13} & -0.18 x_{29} & +  0.43 x_{26}\\
 x_{7}   &  3.53444177769 & +  0.04 x_{19} & -0.99 x_{10} & +  0.03 x_{30} & -0.06 x_{3} & -0.25 x_{5} & -1.72 x_{8} & +  0.48 x_{1} & +  0.06 x_{22} & +  0.08 x_{20} & -0.06 x_{16} & -0.61 x_{11} & +  0.87 x_{12} & +  0.91 x_{13} & +  0.07 x_{29} & -0.07 x_{26}\\
 x_{23}   &  76.9647230272 & -0.32 x_{19} & -6.38 x_{10} & -0.09 x_{30} & +  0.70 x_{3} & + 14.24 x_{5} & -10.84 x_{8} & -2.48 x_{1} & -0.10 x_{22} & -0.45 x_{20} & -0.46 x_{16} & -6.09 x_{11} & +  3.25 x_{12} & + 11.52 x_{13} & +  0.28 x_{29} & -0.86 x_{26}\\
 x_{24}   &  16.832940203 & -1.31 x_{19} & +  8.26 x_{10} & +  0.41 x_{30} & + 10.07 x_{3} & +  2.26 x_{5} & -2.49 x_{8} & +  8.41 x_{1} & +  0.07 x_{22} & -1.51 x_{20} & +  0.29 x_{16} & + 28.91 x_{11} & -20.35 x_{12} & +  6.65 x_{13} & -0.53 x_{29} & +  0.38 x_{26}\\
 x_{15}   &  2.91446872497 & -0.01 x_{19} & +  0.40 x_{10} & +  0.13 x_{30} & +  0.41 x_{3} & -1.70 x_{5} & -1.49 x_{8} & +  0.85 x_{1} & +  0.03 x_{22} & +  0.06 x_{20} & -0.03 x_{16} & +  0.69 x_{11} & -1.75 x_{12} & +  0.93 x_{13} & -0.02 x_{29} & +  0.07 x_{26}\\
 x_{25}   &  61.8137254076 & -0.05 x_{19} & -5.99 x_{10} & +  0.76 x_{30} & -4.26 x_{3} & +  1.00 x_{5} & -28.32 x_{8} & +  0.89 x_{1} & +  1.48 x_{22} & +  1.04 x_{20} & +  0.00 x_{16} & + 15.91 x_{11} & -10.12 x_{12} & + 20.08 x_{13} & +  0.08 x_{29} & -0.26 x_{26}\\
 x_{27}   &  44.8960150595 & +  0.08 x_{19} & + 11.27 x_{10} & -0.57 x_{30} & -10.32 x_{3} & -5.77 x_{5} & + 10.10 x_{8} & -3.97 x_{1} & -0.41 x_{22} & +  0.61 x_{20} & +  0.46 x_{16} & -4.74 x_{11} & -5.30 x_{12} & -12.21 x_{13} & -0.64 x_{29} & +  0.14 x_{26}\\
 x_{28}   &  63.8427544239 & +  0.33 x_{19} & +  0.34 x_{10} & -0.37 x_{30} & -10.65 x_{3} & -8.93 x_{5} & -3.49 x_{8} & -10.78 x_{1} & -0.46 x_{22} & +  0.21 x_{20} & -0.11 x_{16} & -10.01 x_{11} & +  0.33 x_{12} & +  5.93 x_{13} & -0.45 x_{29} & +  0.12 x_{26}\\
 x_{14}   &  1.13276326558 & +  0.02 x_{19} & +  0.17 x_{10} & -0.12 x_{30} & -0.98 x_{3} & +  1.44 x_{5} & +  2.41 x_{8} & -1.52 x_{1} & -0.07 x_{22} & -0.02 x_{20} & +  0.05 x_{16} & -0.86 x_{11} & +  1.21 x_{12} & -1.57 x_{13} & +  0.01 x_{29} & +  0.03 x_{26}\\
 x_{9}   &  3.80381525961 & -0.01 x_{19} & +  0.18 x_{10} & +  0.01 x_{30} & -0.76 x_{3} & +  0.49 x_{5} & -0.87 x_{8} & -0.32 x_{1} & +  0.03 x_{22} & +  0.07 x_{20} & +  0.04 x_{16} & -0.04 x_{11} & +  0.45 x_{12} & +  0.66 x_{13} & +  0.01 x_{29} & -0.05 x_{26}\\
 x_{31}   &  4.94876958258 & -0.22 x_{19} & + 20.80 x_{10} & +  0.17 x_{30} & -0.46 x_{3} & -15.65 x_{5} & +  1.66 x_{8} & -3.19 x_{1} & -0.60 x_{22} & -0.60 x_{20} & +  0.19 x_{16} & +  8.90 x_{11} & -17.98 x_{12} & -5.75 x_{13} & -0.94 x_{29} & +  0.75 x_{26}\\
\hline
z    &  -7.96930059342 & -0.05 x_{19} & -4.94 x_{10} & -0.00 x_{30} & -0.67 x_{3} & -4.91 x_{5} & -2.05 x_{8} & -3.68 x_{1} & +  0.15 x_{22} & -0.08 x_{20} & -0.07 x_{16} & -2.51 x_{11} & -2.81 x_{12} & -3.02 x_{13} & -0.23 x_{29} & +  0.23 x_{26}\\
\end{array}\]


 $ x_{22} $ enters and $ x_{31} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{4}   &  0.759776737991 & +  0.08 x_{19} & -1.59 x_{10} & -0.16 x_{30} & -1.59 x_{3} & +  2.28 x_{5} & +  1.61 x_{8} & -1.02 x_{1} & +  0.08 x_{31} & +  0.04 x_{20} & +  0.02 x_{16} & -1.86 x_{11} & +  3.04 x_{12} & -1.02 x_{13} & +  0.04 x_{29} & -0.08 x_{26}\\
 x_{17}   &  67.5789035567 & +  0.69 x_{19} & -15.06 x_{10} & -3.48 x_{30} & -40.34 x_{3} & + 43.71 x_{5} & + 37.93 x_{8} & -42.83 x_{1} & +  0.55 x_{31} & +  0.27 x_{20} & +  1.39 x_{16} & -30.59 x_{11} & + 50.07 x_{12} & -36.66 x_{13} & +  0.83 x_{29} & -1.19 x_{26}\\
 x_{6}   &  1.42444091846 & +  0.07 x_{19} & -0.83 x_{10} & +  0.02 x_{30} & +  0.25 x_{3} & +  0.27 x_{5} & -0.59 x_{8} & +  0.57 x_{1} & +  0.03 x_{31} & +  0.04 x_{20} & -0.04 x_{16} & -0.88 x_{11} & +  1.10 x_{12} & +  0.24 x_{13} & +  0.06 x_{29} & -0.05 x_{26}\\
 x_{18}   &  51.0573219274 & +  1.05 x_{19} & -14.00 x_{10} & -0.63 x_{30} & -12.00 x_{3} & + 17.46 x_{5} & -22.51 x_{8} & +  8.64 x_{1} & +  0.16 x_{31} & +  1.00 x_{20} & -0.83 x_{16} & -36.15 x_{11} & + 36.83 x_{12} & +  5.80 x_{13} & +  0.55 x_{29} & -2.03 x_{26}\\
 x_{2}   &  0.292391275753 & +  0.01 x_{19} & -1.35 x_{10} & -0.04 x_{30} & -0.08 x_{3} & +  1.48 x_{5} & -0.64 x_{8} & +  0.49 x_{1} & +  0.09 x_{31} & +  0.05 x_{20} & -0.04 x_{16} & -1.82 x_{11} & +  1.91 x_{12} & +  0.87 x_{13} & +  0.04 x_{29} & -0.09 x_{26}\\
 x_{21}   &  27.6026680144 & +  0.33 x_{19} & -4.90 x_{10} & +  0.29 x_{30} & +  6.48 x_{3} & -16.21 x_{5} & -2.57 x_{8} & + 12.12 x_{1} & +  0.05 x_{31} & +  0.68 x_{20} & -0.54 x_{16} & -6.27 x_{11} & -12.75 x_{12} & -4.87 x_{13} & -0.12 x_{29} & +  0.39 x_{26}\\
 x_{7}   &  4.01060219948 & +  0.02 x_{19} & +  1.01 x_{10} & +  0.05 x_{30} & -0.10 x_{3} & -1.75 x_{5} & -1.56 x_{8} & +  0.17 x_{1} & -0.10 x_{31} & +  0.02 x_{20} & -0.04 x_{16} & +  0.24 x_{11} & -0.86 x_{12} & +  0.36 x_{13} & -0.02 x_{29} & +  0.01 x_{26}\\
 x_{23}   &  76.1026208726 & -0.29 x_{19} & -10.00 x_{10} & -0.12 x_{30} & +  0.78 x_{3} & + 16.97 x_{5} & -11.12 x_{8} & -1.92 x_{1} & +  0.17 x_{31} & -0.35 x_{20} & -0.49 x_{16} & -7.64 x_{11} & +  6.39 x_{12} & + 12.52 x_{13} & +  0.44 x_{29} & -0.99 x_{26}\\
 x_{24}   &  17.3941607157 & -1.33 x_{19} & + 10.62 x_{10} & +  0.43 x_{30} & + 10.01 x_{3} & +  0.49 x_{5} & -2.30 x_{8} & +  8.05 x_{1} & -0.11 x_{31} & -1.58 x_{20} & +  0.31 x_{16} & + 29.92 x_{11} & -22.39 x_{12} & +  6.00 x_{13} & -0.63 x_{29} & +  0.47 x_{26}\\
 x_{15}   &  3.17650099574 & -0.02 x_{19} & +  1.50 x_{10} & +  0.14 x_{30} & +  0.39 x_{3} & -2.53 x_{5} & -1.40 x_{8} & +  0.68 x_{1} & -0.05 x_{31} & +  0.03 x_{20} & -0.02 x_{16} & +  1.16 x_{11} & -2.70 x_{12} & +  0.62 x_{13} & -0.07 x_{29} & +  0.11 x_{26}\\
 x_{25}   &  74.008280442 & -0.59 x_{19} & + 45.26 x_{10} & +  1.18 x_{30} & -5.41 x_{3} & -37.58 x_{5} & -24.24 x_{8} & -6.98 x_{1} & -2.46 x_{31} & -0.43 x_{20} & +  0.48 x_{16} & + 37.84 x_{11} & -54.43 x_{12} & +  5.92 x_{13} & -2.23 x_{29} & +  1.58 x_{26}\\
 x_{27}   &  41.5191863268 & +  0.23 x_{19} & -2.92 x_{10} & -0.69 x_{30} & -10.00 x_{3} & +  4.91 x_{5} & +  8.97 x_{8} & -1.79 x_{1} & +  0.68 x_{31} & +  1.01 x_{20} & +  0.33 x_{16} & -10.82 x_{11} & +  6.97 x_{12} & -8.29 x_{13} & +  0.00 x_{29} & -0.37 x_{26}\\
 x_{28}   &  60.063167318 & +  0.49 x_{19} & -15.54 x_{10} & -0.50 x_{30} & -10.29 x_{3} & +  3.03 x_{5} & -4.76 x_{8} & -8.34 x_{1} & +  0.76 x_{31} & +  0.67 x_{20} & -0.25 x_{16} & -16.81 x_{11} & + 14.07 x_{12} & + 10.31 x_{13} & +  0.27 x_{29} & -0.45 x_{26}\\
 x_{14}   &  0.567270766537 & +  0.05 x_{19} & -2.21 x_{10} & -0.14 x_{30} & -0.92 x_{3} & +  3.23 x_{5} & +  2.22 x_{8} & -1.15 x_{1} & +  0.11 x_{31} & +  0.05 x_{20} & +  0.03 x_{16} & -1.88 x_{11} & +  3.26 x_{12} & -0.92 x_{13} & +  0.12 x_{29} & -0.05 x_{26}\\
 x_{9}   &  4.07188941437 & -0.02 x_{19} & +  1.31 x_{10} & +  0.02 x_{30} & -0.79 x_{3} & -0.36 x_{5} & -0.78 x_{8} & -0.49 x_{1} & -0.05 x_{31} & +  0.04 x_{20} & +  0.05 x_{16} & +  0.44 x_{11} & -0.52 x_{12} & +  0.35 x_{13} & -0.04 x_{29} & -0.01 x_{26}\\
 x_{22}   &  8.23706447365 & -0.36 x_{19} & + 34.61 x_{10} & +  0.29 x_{30} & -0.77 x_{3} & -26.06 x_{5} & +  2.76 x_{8} & -5.32 x_{1} & -1.66 x_{31} & -0.99 x_{20} & +  0.32 x_{16} & + 14.81 x_{11} & -29.93 x_{12} & -9.56 x_{13} & -1.57 x_{29} & +  1.24 x_{26}\\
\hline
z    &  -6.69743032087 & -0.10 x_{19} & +  0.41 x_{10} & +  0.04 x_{30} & -0.79 x_{3} & -8.93 x_{5} & -1.63 x_{8} & -4.50 x_{1} & -0.26 x_{31} & -0.23 x_{20} & -0.02 x_{16} & -0.23 x_{11} & -7.43 x_{12} & -4.50 x_{13} & -0.47 x_{29} & +  0.42 x_{26}\\
\end{array}\]


 $ x_{10} $ enters and $ x_{2} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{4}   &  0.414737831238 & +  0.08 x_{19} & +  1.18 x_{2} & -0.11 x_{30} & -1.50 x_{3} & +  0.53 x_{5} & +  2.37 x_{8} & -1.60 x_{1} & -0.03 x_{31} & -0.02 x_{20} & +  0.08 x_{16} & +  0.29 x_{11} & +  0.79 x_{12} & -2.05 x_{13} & -0.02 x_{29} & +  0.03 x_{26}\\
 x_{17}   &  64.3069239783 & +  0.63 x_{19} & + 11.19 x_{2} & -2.97 x_{30} & -39.46 x_{3} & + 27.09 x_{5} & + 45.13 x_{8} & -48.29 x_{1} & -0.47 x_{31} & -0.32 x_{20} & +  1.89 x_{16} & -10.18 x_{11} & + 28.75 x_{12} & -46.42 x_{13} & +  0.33 x_{29} & -0.15 x_{26}\\
 x_{6}   &  1.24377546813 & +  0.07 x_{19} & +  0.62 x_{2} & +  0.05 x_{30} & +  0.30 x_{3} & -0.65 x_{5} & -0.20 x_{8} & +  0.27 x_{1} & -0.03 x_{31} & +  0.01 x_{20} & -0.01 x_{16} & +  0.24 x_{11} & -0.07 x_{12} & -0.30 x_{13} & +  0.03 x_{29} & +  0.00 x_{26}\\
 x_{18}   &  48.0160064435 & +  0.99 x_{19} & + 10.40 x_{2} & -0.16 x_{30} & -11.18 x_{3} & +  2.01 x_{5} & -15.82 x_{8} & +  3.56 x_{1} & -0.78 x_{31} & +  0.46 x_{20} & -0.36 x_{16} & -17.18 x_{11} & + 17.02 x_{12} & -3.26 x_{13} & +  0.09 x_{29} & -1.06 x_{26}\\
 x_{10}   &  0.217220175939 & +  0.00 x_{19} & -0.74 x_{2} & -0.03 x_{30} & -0.06 x_{3} & +  1.10 x_{5} & -0.48 x_{8} & +  0.36 x_{1} & +  0.07 x_{31} & +  0.04 x_{20} & -0.03 x_{16} & -1.36 x_{11} & +  1.42 x_{12} & +  0.65 x_{13} & +  0.03 x_{29} & -0.07 x_{26}\\
 x_{21}   &  26.5379392854 & +  0.31 x_{19} & +  3.64 x_{2} & +  0.45 x_{30} & +  6.76 x_{3} & -21.61 x_{5} & -0.22 x_{8} & + 10.34 x_{1} & -0.28 x_{31} & +  0.49 x_{20} & -0.38 x_{16} & +  0.37 x_{11} & -19.69 x_{12} & -8.04 x_{13} & -0.29 x_{29} & +  0.73 x_{26}\\
 x_{7}   &  4.2305109464 & +  0.02 x_{19} & -0.75 x_{2} & +  0.02 x_{30} & -0.16 x_{3} & -0.64 x_{5} & -2.05 x_{8} & +  0.54 x_{1} & -0.03 x_{31} & +  0.06 x_{20} & -0.08 x_{16} & -1.13 x_{11} & +  0.58 x_{12} & +  1.01 x_{13} & +  0.01 x_{29} & -0.06 x_{26}\\
 x_{23}   &  73.9303977987 & -0.33 x_{19} & +  7.43 x_{2} & +  0.21 x_{30} & +  1.37 x_{3} & +  5.94 x_{5} & -6.34 x_{8} & -5.55 x_{1} & -0.50 x_{31} & -0.73 x_{20} & -0.16 x_{16} & +  5.91 x_{11} & -7.77 x_{12} & +  6.05 x_{13} & +  0.11 x_{29} & -0.30 x_{26}\\
 x_{24}   &  19.7004770206 & -1.29 x_{19} & -7.89 x_{2} & +  0.08 x_{30} & +  9.39 x_{3} & + 12.20 x_{5} & -7.38 x_{8} & + 11.90 x_{1} & +  0.60 x_{31} & -1.17 x_{20} & -0.04 x_{16} & + 15.53 x_{11} & -7.36 x_{12} & + 12.88 x_{13} & -0.28 x_{29} & -0.27 x_{26}\\
 x_{15}   &  3.50170035384 & -0.01 x_{19} & -1.11 x_{2} & +  0.09 x_{30} & +  0.30 x_{3} & -0.88 x_{5} & -2.12 x_{8} & +  1.23 x_{1} & +  0.05 x_{31} & +  0.09 x_{20} & -0.07 x_{16} & -0.87 x_{11} & -0.59 x_{12} & +  1.59 x_{13} & -0.02 x_{29} & +  0.00 x_{26}\\
 x_{25}   &  83.8386893213 & -0.40 x_{19} & -33.62 x_{2} & -0.33 x_{30} & -8.07 x_{3} & + 12.34 x_{5} & -45.88 x_{8} & +  9.44 x_{1} & +  0.59 x_{31} & +  1.33 x_{20} & -1.03 x_{16} & -23.50 x_{11} & +  9.62 x_{12} & + 35.24 x_{13} & -0.73 x_{29} & -1.55 x_{26}\\
 x_{27}   &  40.8854636206 & +  0.22 x_{19} & +  2.17 x_{2} & -0.59 x_{30} & -9.83 x_{3} & +  1.69 x_{5} & + 10.37 x_{8} & -2.84 x_{1} & +  0.49 x_{31} & +  0.90 x_{20} & +  0.43 x_{16} & -6.86 x_{11} & +  2.85 x_{12} & -10.18 x_{13} & -0.09 x_{29} & -0.17 x_{26}\\
 x_{28}   &  56.6876663593 & +  0.43 x_{19} & + 11.54 x_{2} & +  0.02 x_{30} & -9.38 x_{3} & -14.12 x_{5} & +  2.67 x_{8} & -13.97 x_{1} & -0.29 x_{31} & +  0.06 x_{20} & +  0.26 x_{16} & +  4.25 x_{11} & -7.92 x_{12} & +  0.25 x_{13} & -0.25 x_{29} & +  0.62 x_{26}\\
 x_{14}   &  0.0869722945429 & +  0.04 x_{19} & +  1.64 x_{2} & -0.07 x_{30} & -0.79 x_{3} & +  0.79 x_{5} & +  3.28 x_{8} & -1.96 x_{1} & -0.03 x_{31} & -0.03 x_{20} & +  0.11 x_{16} & +  1.12 x_{11} & +  0.13 x_{12} & -2.35 x_{13} & +  0.05 x_{29} & +  0.10 x_{26}\\
 x_{9}   &  4.35639162497 & -0.02 x_{19} & -0.97 x_{2} & -0.02 x_{30} & -0.86 x_{3} & +  1.09 x_{5} & -1.40 x_{8} & -0.02 x_{1} & +  0.03 x_{31} & +  0.09 x_{20} & +  0.00 x_{16} & -1.33 x_{11} & +  1.33 x_{12} & +  1.20 x_{13} & +  0.00 x_{29} & -0.10 x_{26}\\
 x_{22}   &  15.7557940671 & -0.22 x_{19} & -25.71 x_{2} & -0.87 x_{30} & -2.81 x_{3} & + 12.12 x_{5} & -13.79 x_{8} & +  7.24 x_{1} & +  0.67 x_{31} & +  0.36 x_{20} & -0.83 x_{16} & -32.10 x_{11} & + 19.06 x_{12} & + 12.86 x_{13} & -0.41 x_{29} & -1.15 x_{26}\\
\hline
z    &  -6.60897689249 & -0.10 x_{19} & -0.30 x_{2} & +  0.03 x_{30} & -0.82 x_{3} & -8.48 x_{5} & -1.82 x_{8} & -4.36 x_{1} & -0.23 x_{31} & -0.22 x_{20} & -0.03 x_{16} & -0.78 x_{11} & -6.85 x_{12} & -4.24 x_{13} & -0.45 x_{29} & +  0.40 x_{26}\\
\end{array}\]


 $ x_{26} $ enters and $ x_{10} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{4}   &  0.494452594807 & +  0.08 x_{19} & +  0.91 x_{2} & -0.12 x_{30} & -1.52 x_{3} & +  0.93 x_{5} & +  2.20 x_{8} & -1.46 x_{1} & -0.01 x_{31} & -0.00 x_{20} & +  0.06 x_{16} & -0.20 x_{11} & +  1.31 x_{12} & -1.82 x_{13} & -0.01 x_{29} & -0.37 x_{10}\\
 x_{17}   &  63.8348200008 & +  0.62 x_{19} & + 12.81 x_{2} & -2.90 x_{30} & -39.33 x_{3} & + 24.69 x_{5} & + 46.17 x_{8} & -49.08 x_{1} & -0.61 x_{31} & -0.40 x_{20} & +  1.96 x_{16} & -7.23 x_{11} & + 25.68 x_{12} & -47.83 x_{13} & +  0.26 x_{29} & +  2.17 x_{10}\\
 x_{6}   &  1.2518028809 & +  0.07 x_{19} & +  0.59 x_{2} & +  0.04 x_{30} & +  0.29 x_{3} & -0.61 x_{5} & -0.21 x_{8} & +  0.28 x_{1} & -0.02 x_{31} & +  0.01 x_{20} & -0.01 x_{16} & +  0.19 x_{11} & -0.02 x_{12} & -0.28 x_{13} & +  0.03 x_{29} & -0.04 x_{10}\\
 x_{18}   &  44.675266847 & +  0.93 x_{19} & + 21.83 x_{2} & +  0.35 x_{30} & -10.27 x_{3} & -14.95 x_{5} & -8.46 x_{8} & -2.01 x_{1} & -1.82 x_{31} & -0.14 x_{20} & +  0.15 x_{16} & +  3.67 x_{11} & -4.75 x_{12} & -13.23 x_{13} & -0.42 x_{29} & + 15.38 x_{10}\\
 x_{26}   &  3.14188027839 & +  0.06 x_{19} & -10.75 x_{2} & -0.48 x_{30} & -0.85 x_{3} & + 15.95 x_{5} & -6.92 x_{8} & +  5.25 x_{1} & +  0.98 x_{31} & +  0.56 x_{20} & -0.48 x_{16} & -19.60 x_{11} & + 20.47 x_{12} & +  9.37 x_{13} & +  0.48 x_{29} & -14.46 x_{10}\\
 x_{21}   &  28.8374219267 & +  0.35 x_{19} & -4.22 x_{2} & +  0.10 x_{30} & +  6.14 x_{3} & -9.94 x_{5} & -5.29 x_{8} & + 14.18 x_{1} & +  0.44 x_{31} & +  0.91 x_{20} & -0.73 x_{16} & -13.98 x_{11} & -4.71 x_{12} & -1.19 x_{13} & +  0.06 x_{29} & -10.59 x_{10}\\
 x_{7}   &  4.02693333829 & +  0.02 x_{19} & -0.06 x_{2} & +  0.05 x_{30} & -0.11 x_{3} & -1.67 x_{5} & -1.60 x_{8} & +  0.20 x_{1} & -0.09 x_{31} & +  0.02 x_{20} & -0.05 x_{16} & +  0.14 x_{11} & -0.75 x_{12} & +  0.41 x_{13} & -0.02 x_{29} & +  0.94 x_{10}\\
 x_{23}   &  73.000678853 & -0.34 x_{19} & + 10.61 x_{2} & +  0.35 x_{30} & +  1.62 x_{3} & +  1.22 x_{5} & -4.30 x_{8} & -7.10 x_{1} & -0.79 x_{31} & -0.90 x_{20} & -0.02 x_{16} & + 11.71 x_{11} & -13.83 x_{12} & +  3.27 x_{13} & -0.03 x_{29} & +  4.28 x_{10}\\
 x_{24}   &  18.8605689572 & -1.31 x_{19} & -5.02 x_{2} & +  0.20 x_{30} & +  9.62 x_{3} & +  7.93 x_{5} & -5.53 x_{8} & + 10.50 x_{1} & +  0.34 x_{31} & -1.32 x_{20} & +  0.08 x_{16} & + 20.77 x_{11} & -12.84 x_{12} & + 10.37 x_{13} & -0.41 x_{29} & +  3.87 x_{10}\\
 x_{15}   &  3.51017350988 & -0.01 x_{19} & -1.14 x_{2} & +  0.08 x_{30} & +  0.30 x_{3} & -0.84 x_{5} & -2.14 x_{8} & +  1.24 x_{1} & +  0.05 x_{31} & +  0.09 x_{20} & -0.07 x_{16} & -0.92 x_{11} & -0.53 x_{12} & +  1.62 x_{13} & -0.02 x_{29} & -0.04 x_{10}\\
 x_{25}   &  78.970380137 & -0.49 x_{19} & -16.97 x_{2} & +  0.42 x_{30} & -6.75 x_{3} & -12.38 x_{5} & -35.17 x_{8} & +  1.31 x_{1} & -0.92 x_{31} & +  0.46 x_{20} & -0.28 x_{16} & +  6.88 x_{11} & -22.10 x_{12} & + 20.72 x_{13} & -1.47 x_{29} & + 22.41 x_{10}\\
 x_{27}   &  40.3536555925 & +  0.21 x_{19} & +  3.99 x_{2} & -0.51 x_{30} & -9.68 x_{3} & -1.01 x_{5} & + 11.54 x_{8} & -3.73 x_{1} & +  0.32 x_{31} & +  0.80 x_{20} & +  0.51 x_{16} & -3.54 x_{11} & -0.62 x_{12} & -11.77 x_{13} & -0.17 x_{29} & +  2.45 x_{10}\\
 x_{28}   &  58.6506713217 & +  0.47 x_{19} & +  4.83 x_{2} & -0.28 x_{30} & -9.91 x_{3} & -4.15 x_{5} & -1.65 x_{8} & -10.69 x_{1} & +  0.32 x_{31} & +  0.42 x_{20} & -0.04 x_{16} & -7.99 x_{11} & +  4.87 x_{12} & +  6.10 x_{13} & +  0.06 x_{29} & -9.04 x_{10}\\
 x_{14}   &  0.403069488549 & +  0.04 x_{19} & +  0.56 x_{2} & -0.12 x_{30} & -0.88 x_{3} & +  2.40 x_{5} & +  2.59 x_{8} & -1.43 x_{1} & +  0.06 x_{31} & +  0.02 x_{20} & +  0.06 x_{16} & -0.85 x_{11} & +  2.19 x_{12} & -1.41 x_{13} & +  0.10 x_{29} & -1.46 x_{10}\\
 x_{9}   &  4.0273315712 & -0.02 x_{19} & +  0.15 x_{2} & +  0.03 x_{30} & -0.77 x_{3} & -0.58 x_{5} & -0.68 x_{8} & -0.56 x_{1} & -0.07 x_{31} & +  0.03 x_{20} & +  0.05 x_{16} & +  0.72 x_{11} & -0.81 x_{12} & +  0.22 x_{13} & -0.05 x_{29} & +  1.51 x_{10}\\
 x_{22}   &  12.1469933415 & -0.29 x_{19} & -13.37 x_{2} & -0.31 x_{30} & -1.83 x_{3} & -6.20 x_{5} & -5.85 x_{8} & +  1.21 x_{1} & -0.45 x_{31} & -0.29 x_{20} & -0.28 x_{16} & -9.58 x_{11} & -4.46 x_{12} & +  2.10 x_{13} & -0.97 x_{29} & + 16.61 x_{10}\\
\hline
z    &  -5.36470707183 & -0.08 x_{19} & -4.56 x_{2} & -0.16 x_{30} & -1.15 x_{3} & -2.17 x_{5} & -4.56 x_{8} & -2.28 x_{1} & +  0.16 x_{31} & +  0.01 x_{20} & -0.22 x_{16} & -8.54 x_{11} & +  1.26 x_{12} & -0.53 x_{13} & -0.26 x_{29} & -5.73 x_{10}\\
\end{array}\]


 $ x_{12} $ enters and $ x_{24} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{4}   &  2.41529560184 & -0.05 x_{19} & +  0.40 x_{2} & -0.10 x_{30} & -0.54 x_{3} & +  1.74 x_{5} & +  1.64 x_{8} & -0.40 x_{1} & +  0.03 x_{31} & -0.14 x_{20} & +  0.07 x_{16} & +  1.91 x_{11} & -0.10 x_{24} & -0.76 x_{13} & -0.05 x_{29} & +  0.03 x_{10}\\
 x_{17}   &  101.561544079 & -1.99 x_{19} & +  2.77 x_{2} & -2.49 x_{30} & -20.09 x_{3} & + 40.56 x_{5} & + 35.12 x_{8} & -28.09 x_{1} & +  0.07 x_{31} & -3.04 x_{20} & +  2.13 x_{16} & + 34.32 x_{11} & -2.00 x_{24} & -27.08 x_{13} & -0.56 x_{29} & +  9.91 x_{10}\\
 x_{6}   &  1.21874976892 & +  0.07 x_{19} & +  0.60 x_{2} & +  0.04 x_{30} & +  0.28 x_{3} & -0.62 x_{5} & -0.20 x_{8} & +  0.26 x_{1} & -0.02 x_{31} & +  0.01 x_{20} & -0.01 x_{16} & +  0.16 x_{11} & +  0.00 x_{24} & -0.30 x_{13} & +  0.03 x_{29} & -0.04 x_{10}\\
 x_{18}   &  37.696977849 & +  1.42 x_{19} & + 23.68 x_{2} & +  0.28 x_{30} & -13.83 x_{3} & -17.89 x_{5} & -6.42 x_{8} & -5.90 x_{1} & -1.95 x_{31} & +  0.35 x_{20} & +  0.12 x_{16} & -4.02 x_{11} & +  0.37 x_{24} & -17.07 x_{13} & -0.27 x_{29} & + 13.95 x_{10}\\
 x_{26}   &  33.2219600298 & -2.03 x_{19} & -18.74 x_{2} & -0.16 x_{30} & + 14.49 x_{3} & + 28.61 x_{5} & -15.73 x_{8} & + 21.99 x_{1} & +  1.52 x_{31} & -1.54 x_{20} & -0.35 x_{16} & + 13.52 x_{11} & -1.59 x_{24} & + 25.92 x_{13} & -0.17 x_{29} & -8.30 x_{10}\\
 x_{21}   &  21.9210355075 & +  0.83 x_{19} & -2.38 x_{2} & +  0.02 x_{30} & +  2.61 x_{3} & -12.85 x_{5} & -3.26 x_{8} & + 10.34 x_{1} & +  0.31 x_{31} & +  1.39 x_{20} & -0.76 x_{16} & -21.59 x_{11} & +  0.37 x_{24} & -4.99 x_{13} & +  0.21 x_{29} & -12.00 x_{10}\\
 x_{7}   &  2.92522963963 & +  0.09 x_{19} & +  0.24 x_{2} & +  0.04 x_{30} & -0.67 x_{3} & -2.13 x_{5} & -1.28 x_{8} & -0.41 x_{1} & -0.11 x_{31} & +  0.10 x_{20} & -0.05 x_{16} & -1.07 x_{11} & +  0.06 x_{24} & -0.20 x_{13} & +  0.00 x_{29} & +  0.71 x_{10}\\
 x_{23}   &  52.6861383056 & +  1.06 x_{19} & + 16.01 x_{2} & +  0.13 x_{30} & -8.74 x_{3} & -7.33 x_{5} & +  1.66 x_{8} & -18.40 x_{1} & -1.16 x_{31} & +  0.52 x_{20} & -0.11 x_{16} & -10.66 x_{11} & +  1.08 x_{24} & -7.90 x_{13} & +  0.41 x_{29} & +  0.12 x_{10}\\
 x_{12}   &  1.46935362686 & -0.10 x_{19} & -0.39 x_{2} & +  0.02 x_{30} & +  0.75 x_{3} & +  0.62 x_{5} & -0.43 x_{8} & +  0.82 x_{1} & +  0.03 x_{31} & -0.10 x_{20} & +  0.01 x_{16} & +  1.62 x_{11} & -0.08 x_{24} & +  0.81 x_{13} & -0.03 x_{29} & +  0.30 x_{10}\\
 x_{15}   &  2.73150167646 & +  0.04 x_{19} & -0.93 x_{2} & +  0.08 x_{30} & -0.10 x_{3} & -1.16 x_{5} & -1.91 x_{8} & +  0.81 x_{1} & +  0.04 x_{31} & +  0.14 x_{20} & -0.07 x_{16} & -1.78 x_{11} & +  0.04 x_{24} & +  1.19 x_{13} & -0.00 x_{29} & -0.20 x_{10}\\
 x_{25}   &  46.4971028804 & +  1.75 x_{19} & -8.34 x_{2} & +  0.07 x_{30} & -23.31 x_{3} & -26.04 x_{5} & -25.65 x_{8} & -16.76 x_{1} & -1.51 x_{31} & +  2.73 x_{20} & -0.43 x_{16} & -28.88 x_{11} & +  1.72 x_{24} & +  2.86 x_{13} & -0.77 x_{29} & + 15.75 x_{10}\\
 x_{27}   &  39.4427349291 & +  0.27 x_{19} & +  4.23 x_{2} & -0.52 x_{30} & -10.15 x_{3} & -1.39 x_{5} & + 11.80 x_{8} & -4.24 x_{1} & +  0.30 x_{31} & +  0.87 x_{20} & +  0.50 x_{16} & -4.55 x_{11} & +  0.05 x_{24} & -12.27 x_{13} & -0.16 x_{29} & +  2.26 x_{10}\\
 x_{28}   &  65.8004851118 & -0.03 x_{19} & +  2.93 x_{2} & -0.20 x_{30} & -6.27 x_{3} & -1.14 x_{5} & -3.74 x_{8} & -6.72 x_{1} & +  0.45 x_{31} & -0.08 x_{20} & -0.01 x_{16} & -0.12 x_{11} & -0.38 x_{24} & + 10.03 x_{13} & -0.10 x_{29} & -7.57 x_{10}\\
 x_{14}   &  3.62133051613 & -0.18 x_{19} & -0.29 x_{2} & -0.08 x_{30} & +  0.76 x_{3} & +  3.75 x_{5} & +  1.64 x_{8} & +  0.36 x_{1} & +  0.12 x_{31} & -0.20 x_{20} & +  0.07 x_{16} & +  2.69 x_{11} & -0.17 x_{24} & +  0.36 x_{13} & +  0.03 x_{29} & -0.80 x_{10}\\
 x_{9}   &  2.83487431107 & +  0.06 x_{19} & +  0.47 x_{2} & +  0.01 x_{30} & -1.38 x_{3} & -1.08 x_{5} & -0.33 x_{8} & -1.23 x_{1} & -0.09 x_{31} & +  0.12 x_{20} & +  0.05 x_{16} & -0.59 x_{11} & +  0.06 x_{24} & -0.44 x_{13} & -0.02 x_{29} & +  1.27 x_{10}\\
 x_{22}   &  5.59561611835 & +  0.16 x_{19} & -11.63 x_{2} & -0.38 x_{30} & -5.17 x_{3} & -8.96 x_{5} & -3.93 x_{8} & -2.43 x_{1} & -0.57 x_{31} & +  0.17 x_{20} & -0.31 x_{16} & -16.80 x_{11} & +  0.35 x_{24} & -1.51 x_{13} & -0.82 x_{29} & + 15.27 x_{10}\\
\hline
z    &  -3.5188096162 & -0.21 x_{19} & -5.05 x_{2} & -0.14 x_{30} & -0.21 x_{3} & -1.39 x_{5} & -5.10 x_{8} & -1.25 x_{1} & +  0.19 x_{31} & -0.12 x_{20} & -0.21 x_{16} & -6.51 x_{11} & -0.10 x_{24} & +  0.49 x_{13} & -0.30 x_{29} & -5.35 x_{10}\\
\end{array}\]


 $ x_{13} $ enters and $ x_{18} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{4}   &  0.737770045864 & -0.12 x_{19} & -0.66 x_{2} & -0.11 x_{30} & +  0.08 x_{3} & +  2.54 x_{5} & +  1.92 x_{8} & -0.13 x_{1} & +  0.11 x_{31} & -0.15 x_{20} & +  0.07 x_{16} & +  2.09 x_{11} & -0.12 x_{24} & +  0.04 x_{18} & -0.03 x_{29} & -0.59 x_{10}\\
 x_{17}   &  41.7488554838 & -4.24 x_{19} & -34.80 x_{2} & -2.93 x_{30} & +  1.85 x_{3} & + 68.95 x_{5} & + 45.30 x_{8} & -18.73 x_{1} & +  3.16 x_{31} & -3.59 x_{20} & +  1.94 x_{16} & + 40.69 x_{11} & -2.59 x_{24} & +  1.59 x_{18} & -0.12 x_{29} & -12.22 x_{10}\\
 x_{6}   &  0.564832206358 & +  0.05 x_{19} & +  0.19 x_{2} & +  0.04 x_{30} & +  0.52 x_{3} & -0.31 x_{5} & -0.09 x_{8} & +  0.36 x_{1} & +  0.01 x_{31} & +  0.00 x_{20} & -0.01 x_{16} & +  0.23 x_{11} & -0.00 x_{24} & +  0.02 x_{18} & +  0.04 x_{29} & -0.29 x_{10}\\
 x_{13}   &  2.20898045129 & +  0.08 x_{19} & +  1.39 x_{2} & +  0.02 x_{30} & -0.81 x_{3} & -1.05 x_{5} & -0.38 x_{8} & -0.35 x_{1} & -0.11 x_{31} & +  0.02 x_{20} & +  0.01 x_{16} & -0.24 x_{11} & +  0.02 x_{24} & -0.06 x_{18} & -0.02 x_{29} & +  0.82 x_{10}\\
 x_{26}   &  90.4695309685 & +  0.13 x_{19} & + 17.22 x_{2} & +  0.27 x_{30} & -6.52 x_{3} & +  1.44 x_{5} & -25.48 x_{8} & + 13.03 x_{1} & -1.43 x_{31} & -1.01 x_{20} & -0.17 x_{16} & +  7.42 x_{11} & -1.03 x_{24} & -1.52 x_{18} & -0.59 x_{29} & + 12.89 x_{10}\\
 x_{21}   &  10.8987079931 & +  0.42 x_{19} & -9.31 x_{2} & -0.06 x_{30} & +  6.66 x_{3} & -7.62 x_{5} & -1.38 x_{8} & + 12.06 x_{1} & +  0.88 x_{31} & +  1.29 x_{20} & -0.80 x_{16} & -20.42 x_{11} & +  0.26 x_{24} & +  0.29 x_{18} & +  0.29 x_{29} & -16.08 x_{10}\\
 x_{7}   &  2.48601678676 & +  0.08 x_{19} & -0.04 x_{2} & +  0.03 x_{30} & -0.51 x_{3} & -1.93 x_{5} & -1.20 x_{8} & -0.34 x_{1} & -0.09 x_{31} & +  0.09 x_{20} & -0.05 x_{16} & -1.03 x_{11} & +  0.05 x_{24} & +  0.01 x_{18} & +  0.01 x_{29} & +  0.55 x_{10}\\
 x_{23}   &  35.2346730959 & +  0.41 x_{19} & +  5.05 x_{2} & +  0.00 x_{30} & -2.33 x_{3} & +  0.95 x_{5} & +  4.63 x_{8} & -15.67 x_{1} & -0.26 x_{31} & +  0.36 x_{20} & -0.16 x_{16} & -8.80 x_{11} & +  0.91 x_{24} & +  0.46 x_{18} & +  0.54 x_{29} & -6.34 x_{10}\\
 x_{12}   &  3.25480572459 & -0.03 x_{19} & +  0.73 x_{2} & +  0.03 x_{30} & +  0.09 x_{3} & -0.23 x_{5} & -0.73 x_{8} & +  0.54 x_{1} & -0.07 x_{31} & -0.09 x_{20} & +  0.01 x_{16} & +  1.43 x_{11} & -0.06 x_{24} & -0.05 x_{18} & -0.04 x_{29} & +  0.96 x_{10}\\
 x_{15}   &  5.35656061047 & +  0.14 x_{19} & +  0.72 x_{2} & +  0.09 x_{30} & -1.06 x_{3} & -2.41 x_{5} & -2.36 x_{8} & +  0.40 x_{1} & -0.10 x_{31} & +  0.17 x_{20} & -0.06 x_{16} & -2.06 x_{11} & +  0.07 x_{24} & -0.07 x_{18} & -0.02 x_{29} & +  0.77 x_{10}\\
 x_{25}   &  52.8063921101 & +  1.99 x_{19} & -4.37 x_{2} & +  0.12 x_{30} & -25.62 x_{3} & -29.04 x_{5} & -26.72 x_{8} & -17.75 x_{1} & -1.84 x_{31} & +  2.79 x_{20} & -0.41 x_{16} & -29.55 x_{11} & +  1.78 x_{24} & -0.17 x_{18} & -0.81 x_{29} & + 18.09 x_{10}\\
 x_{27}   &  12.3394208724 & -0.75 x_{19} & -12.80 x_{2} & -0.72 x_{30} & -0.20 x_{3} & + 11.47 x_{5} & + 16.42 x_{8} & +  0.00 x_{1} & +  1.70 x_{31} & +  0.62 x_{20} & +  0.42 x_{16} & -1.66 x_{11} & -0.22 x_{24} & +  0.72 x_{18} & +  0.04 x_{29} & -7.77 x_{10}\\
 x_{28}   &  87.9669387821 & +  0.80 x_{19} & + 16.86 x_{2} & -0.04 x_{30} & -14.40 x_{3} & -11.66 x_{5} & -7.52 x_{8} & -10.18 x_{1} & -0.69 x_{31} & +  0.12 x_{20} & +  0.07 x_{16} & -2.48 x_{11} & -0.16 x_{24} & -0.59 x_{18} & -0.26 x_{29} & +  0.63 x_{10}\\
 x_{14}   &  4.42147647312 & -0.15 x_{19} & +  0.21 x_{2} & -0.08 x_{30} & +  0.47 x_{3} & +  3.37 x_{5} & +  1.51 x_{8} & +  0.24 x_{1} & +  0.08 x_{31} & -0.19 x_{20} & +  0.07 x_{16} & +  2.61 x_{11} & -0.16 x_{24} & -0.02 x_{18} & +  0.02 x_{29} & -0.50 x_{10}\\
 x_{9}   &  1.86223579152 & +  0.02 x_{19} & -0.14 x_{2} & +  0.01 x_{30} & -1.03 x_{3} & -0.62 x_{5} & -0.16 x_{8} & -1.08 x_{1} & -0.04 x_{31} & +  0.11 x_{20} & +  0.05 x_{16} & -0.49 x_{11} & +  0.05 x_{24} & +  0.03 x_{18} & -0.01 x_{29} & +  0.91 x_{10}\\
 x_{22}   &  2.2654656138 & +  0.04 x_{19} & -13.72 x_{2} & -0.41 x_{30} & -3.95 x_{3} & -7.38 x_{5} & -3.36 x_{8} & -1.91 x_{1} & -0.40 x_{31} & +  0.14 x_{20} & -0.32 x_{16} & -16.44 x_{11} & +  0.31 x_{24} & +  0.09 x_{18} & -0.80 x_{29} & + 14.04 x_{10}\\
\hline
z    &  -2.43969617893 & -0.17 x_{19} & -4.37 x_{2} & -0.13 x_{30} & -0.61 x_{3} & -1.90 x_{5} & -5.29 x_{8} & -1.42 x_{1} & +  0.13 x_{31} & -0.11 x_{20} & -0.21 x_{16} & -6.62 x_{11} & -0.09 x_{24} & -0.03 x_{18} & -0.31 x_{29} & -4.95 x_{10}\\
\end{array}\]


 $ x_{31} $ enters and $ x_{22} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{4}   &  1.38901417944 & -0.11 x_{19} & -4.60 x_{2} & -0.23 x_{30} & -1.06 x_{3} & +  0.42 x_{5} & +  0.96 x_{8} & -0.68 x_{1} & -0.29 x_{22} & -0.11 x_{20} & -0.02 x_{16} & -2.64 x_{11} & -0.03 x_{24} & +  0.07 x_{18} & -0.26 x_{29} & +  3.44 x_{10}\\
 x_{17}   &  59.7841422156 & -3.93 x_{19} & -144.05 x_{2} & -6.18 x_{30} & -29.59 x_{3} & + 10.21 x_{5} & + 18.53 x_{8} & -33.96 x_{1} & -7.96 x_{22} & -2.51 x_{20} & -0.59 x_{16} & -90.20 x_{11} & -0.08 x_{24} & +  2.29 x_{18} & -6.49 x_{29} & + 99.53 x_{10}\\
 x_{6}   &  0.623518751837 & +  0.05 x_{19} & -0.17 x_{2} & +  0.03 x_{30} & +  0.41 x_{3} & -0.50 x_{5} & -0.18 x_{8} & +  0.32 x_{1} & -0.03 x_{22} & +  0.01 x_{20} & -0.02 x_{16} & -0.20 x_{11} & +  0.00 x_{24} & +  0.02 x_{18} & +  0.02 x_{29} & +  0.08 x_{10}\\
 x_{13}   &  1.55769639369 & +  0.07 x_{19} & +  5.33 x_{2} & +  0.13 x_{30} & +  0.32 x_{3} & +  1.07 x_{5} & +  0.59 x_{8} & +  0.20 x_{1} & +  0.29 x_{22} & -0.02 x_{20} & +  0.10 x_{16} & +  4.49 x_{11} & -0.07 x_{24} & -0.08 x_{18} & +  0.21 x_{29} & -3.22 x_{10}\\
 x_{26}   &  82.2846841548 & -0.02 x_{19} & + 66.80 x_{2} & +  1.74 x_{30} & +  7.75 x_{3} & + 28.10 x_{5} & -13.33 x_{8} & + 19.94 x_{1} & +  3.61 x_{22} & -1.50 x_{20} & +  0.98 x_{16} & + 66.82 x_{11} & -2.17 x_{24} & -1.84 x_{18} & +  2.30 x_{29} & -37.83 x_{10}\\
 x_{21}   &  15.9349196553 & +  0.50 x_{19} & -39.81 x_{2} & -0.96 x_{30} & -2.12 x_{3} & -24.02 x_{5} & -8.86 x_{8} & +  7.81 x_{1} & -2.22 x_{22} & +  1.59 x_{20} & -1.50 x_{16} & -56.97 x_{11} & +  0.96 x_{24} & +  0.49 x_{18} & -1.48 x_{29} & + 15.13 x_{10}\\
 x_{7}   &  1.98070848061 & +  0.07 x_{19} & +  3.02 x_{2} & +  0.12 x_{30} & +  0.37 x_{3} & -0.28 x_{5} & -0.45 x_{8} & +  0.08 x_{1} & +  0.22 x_{22} & +  0.06 x_{20} & +  0.02 x_{16} & +  2.64 x_{11} & -0.02 x_{24} & -0.01 x_{18} & +  0.18 x_{29} & -2.58 x_{10}\\
 x_{23}   &  33.7643313556 & +  0.38 x_{19} & + 13.95 x_{2} & +  0.27 x_{30} & +  0.23 x_{3} & +  5.74 x_{5} & +  6.81 x_{8} & -14.43 x_{1} & +  0.65 x_{22} & +  0.27 x_{20} & +  0.04 x_{16} & +  1.87 x_{11} & +  0.70 x_{24} & +  0.41 x_{18} & +  1.05 x_{29} & -15.45 x_{10}\\
 x_{12}   &  2.88068056426 & -0.04 x_{19} & +  3.00 x_{2} & +  0.10 x_{30} & +  0.75 x_{3} & +  0.99 x_{5} & -0.18 x_{8} & +  0.85 x_{1} & +  0.17 x_{22} & -0.11 x_{20} & +  0.06 x_{16} & +  4.14 x_{11} & -0.11 x_{24} & -0.06 x_{18} & +  0.09 x_{29} & -1.36 x_{10}\\
 x_{15}   &  4.79164427785 & +  0.13 x_{19} & +  4.14 x_{2} & +  0.20 x_{30} & -0.08 x_{3} & -0.57 x_{5} & -1.52 x_{8} & +  0.88 x_{1} & +  0.25 x_{22} & +  0.13 x_{20} & +  0.01 x_{16} & +  2.04 x_{11} & -0.01 x_{24} & -0.09 x_{18} & +  0.18 x_{29} & -2.73 x_{10}\\
 x_{25}   &  42.3117355482 & +  1.81 x_{19} & + 59.20 x_{2} & +  2.00 x_{30} & -7.33 x_{3} & +  5.14 x_{5} & -11.15 x_{8} & -8.89 x_{1} & +  4.63 x_{22} & +  2.16 x_{20} & +  1.06 x_{16} & + 46.61 x_{11} & +  0.33 x_{24} & -0.58 x_{18} & +  2.89 x_{29} & -46.94 x_{10}\\
 x_{27}   &  22.0651245681 & -0.58 x_{19} & -71.71 x_{2} & -2.47 x_{30} & -17.16 x_{3} & -20.21 x_{5} & +  1.98 x_{8} & -8.21 x_{1} & -4.29 x_{22} & +  1.20 x_{20} & -0.94 x_{16} & -72.25 x_{11} & +  1.13 x_{24} & +  1.10 x_{18} & -3.39 x_{29} & + 52.50 x_{10}\\
 x_{28}   &  84.0282157267 & +  0.74 x_{19} & + 40.71 x_{2} & +  0.67 x_{30} & -7.53 x_{3} & +  1.17 x_{5} & -1.67 x_{8} & -6.86 x_{1} & +  1.74 x_{22} & -0.11 x_{20} & +  0.62 x_{16} & + 26.10 x_{11} & -0.71 x_{24} & -0.74 x_{18} & +  1.13 x_{29} & -23.78 x_{10}\\
 x_{14}   &  4.88040952342 & -0.14 x_{19} & -2.57 x_{2} & -0.16 x_{30} & -0.33 x_{3} & +  1.87 x_{5} & +  0.83 x_{8} & -0.15 x_{1} & -0.20 x_{22} & -0.17 x_{20} & +  0.01 x_{16} & -0.72 x_{11} & -0.10 x_{24} & -0.00 x_{18} & -0.14 x_{29} & +  2.34 x_{10}\\
 x_{9}   &  1.63691124975 & +  0.02 x_{19} & +  1.22 x_{2} & +  0.05 x_{30} & -0.63 x_{3} & +  0.11 x_{5} & +  0.17 x_{8} & -0.89 x_{1} & +  0.10 x_{22} & +  0.10 x_{20} & +  0.08 x_{16} & +  1.15 x_{11} & +  0.02 x_{24} & +  0.02 x_{18} & +  0.07 x_{29} & -0.49 x_{10}\\
 x_{31}   &  5.71207261785 & +  0.10 x_{19} & -34.60 x_{2} & -1.03 x_{30} & -9.96 x_{3} & -18.60 x_{5} & -8.48 x_{8} & -4.82 x_{1} & -2.52 x_{22} & +  0.34 x_{20} & -0.80 x_{16} & -41.46 x_{11} & +  0.79 x_{24} & +  0.22 x_{18} & -2.02 x_{29} & + 35.40 x_{10}\\
\hline
z    &  -1.66930045195 & -0.15 x_{19} & -9.04 x_{2} & -0.27 x_{30} & -1.95 x_{3} & -4.41 x_{5} & -6.43 x_{8} & -2.07 x_{1} & -0.34 x_{22} & -0.07 x_{20} & -0.32 x_{16} & -12.22 x_{11} & +  0.02 x_{24} & +  0.00 x_{18} & -0.58 x_{29} & -0.18 x_{10}\\
\end{array}\]


 $ x_{18} $ enters and $ x_{13} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{4}   &  2.68523019675 & -0.05 x_{19} & -0.16 x_{2} & -0.12 x_{30} & -0.79 x_{3} & +  1.31 x_{5} & +  1.45 x_{8} & -0.51 x_{1} & -0.05 x_{22} & -0.13 x_{20} & +  0.06 x_{16} & +  1.10 x_{11} & -0.09 x_{24} & -0.83 x_{13} & -0.09 x_{29} & +  0.76 x_{10}\\
 x_{17}   &  102.251549396 & -1.97 x_{19} & +  1.34 x_{2} & -2.54 x_{30} & -20.73 x_{3} & + 39.46 x_{5} & + 34.63 x_{8} & -28.39 x_{1} & -0.12 x_{22} & -3.02 x_{20} & +  2.09 x_{16} & + 32.24 x_{11} & -1.96 x_{24} & -27.26 x_{13} & -0.66 x_{29} & + 11.79 x_{10}\\
 x_{6}   &  0.987655731308 & +  0.07 x_{19} & +  1.08 x_{2} & +  0.06 x_{30} & +  0.49 x_{3} & -0.25 x_{5} & -0.04 x_{8} & +  0.36 x_{1} & +  0.04 x_{22} & +  0.00 x_{20} & +  0.00 x_{16} & +  0.85 x_{11} & -0.01 x_{24} & -0.23 x_{13} & +  0.07 x_{29} & -0.67 x_{10}\\
 x_{18}   &  18.5451892245 & +  0.85 x_{19} & + 63.49 x_{2} & +  1.59 x_{30} & +  3.87 x_{3} & + 12.77 x_{5} & +  7.03 x_{8} & +  2.43 x_{1} & +  3.42 x_{22} & -0.22 x_{20} & +  1.17 x_{16} & + 53.47 x_{11} & -0.82 x_{24} & -11.91 x_{13} & +  2.55 x_{29} & -38.32 x_{10}\\
 x_{26}   &  48.2025879815 & -1.59 x_{19} & -49.88 x_{2} & -1.18 x_{30} & +  0.64 x_{3} & +  4.63 x_{5} & -26.25 x_{8} & + 15.47 x_{1} & -2.68 x_{22} & -1.09 x_{20} & -1.17 x_{16} & -31.45 x_{11} & -0.66 x_{24} & + 21.88 x_{13} & -2.38 x_{29} & + 32.58 x_{10}\\
 x_{21}   &  24.999360109 & +  0.92 x_{19} & -8.78 x_{2} & -0.19 x_{30} & -0.23 x_{3} & -17.78 x_{5} & -5.42 x_{8} & +  9.00 x_{1} & -0.55 x_{22} & +  1.48 x_{20} & -0.93 x_{16} & -30.83 x_{11} & +  0.56 x_{24} & -5.82 x_{13} & -0.24 x_{29} & -3.60 x_{10}\\
 x_{7}   &  1.83136511958 & +  0.06 x_{19} & +  2.51 x_{2} & +  0.11 x_{30} & +  0.34 x_{3} & -0.38 x_{5} & -0.51 x_{8} & +  0.06 x_{1} & +  0.20 x_{22} & +  0.07 x_{20} & +  0.01 x_{16} & +  2.21 x_{11} & -0.01 x_{24} & +  0.10 x_{13} & +  0.16 x_{29} & -2.27 x_{10}\\
 x_{23}   &  41.28636987 & +  0.73 x_{19} & + 39.70 x_{2} & +  0.91 x_{30} & +  1.80 x_{3} & + 10.92 x_{5} & +  9.66 x_{8} & -13.45 x_{1} & +  2.04 x_{22} & +  0.18 x_{20} & +  0.52 x_{16} & + 23.56 x_{11} & +  0.37 x_{24} & -4.83 x_{13} & +  2.09 x_{29} & -30.99 x_{10}\\
 x_{12}   &  1.73176946959 & -0.09 x_{19} & -0.94 x_{2} & -0.00 x_{30} & +  0.51 x_{3} & +  0.20 x_{5} & -0.61 x_{8} & +  0.70 x_{1} & -0.05 x_{22} & -0.09 x_{20} & -0.01 x_{16} & +  0.83 x_{11} & -0.06 x_{24} & +  0.74 x_{13} & -0.07 x_{29} & +  1.02 x_{10}\\
 x_{15}   &  3.09171351095 & +  0.05 x_{19} & -1.68 x_{2} & +  0.05 x_{30} & -0.43 x_{3} & -1.74 x_{5} & -2.16 x_{8} & +  0.65 x_{1} & -0.06 x_{22} & +  0.15 x_{20} & -0.09 x_{16} & -2.86 x_{11} & +  0.06 x_{24} & +  1.09 x_{13} & -0.06 x_{29} & +  0.78 x_{10}\\
 x_{25}   &  31.6185951523 & +  1.32 x_{19} & + 22.59 x_{2} & +  1.09 x_{30} & -9.56 x_{3} & -2.22 x_{5} & -15.20 x_{8} & -10.29 x_{1} & +  2.66 x_{22} & +  2.29 x_{20} & +  0.39 x_{16} & + 15.78 x_{11} & +  0.80 x_{24} & +  6.86 x_{13} & +  1.42 x_{29} & -24.85 x_{10}\\
 x_{27}   &  42.4319025092 & +  0.36 x_{19} & -1.98 x_{2} & -0.73 x_{30} & -12.91 x_{3} & -6.18 x_{5} & +  9.70 x_{8} & -5.54 x_{1} & -0.53 x_{22} & +  0.96 x_{20} & +  0.34 x_{16} & -13.52 x_{11} & +  0.23 x_{24} & -13.07 x_{13} & -0.60 x_{29} & + 10.42 x_{10}\\
 x_{28}   &  70.2750287004 & +  0.10 x_{19} & -6.37 x_{2} & -0.51 x_{30} & -10.40 x_{3} & -8.30 x_{5} & -6.89 x_{8} & -8.66 x_{1} & -0.80 x_{22} & +  0.05 x_{20} & -0.25 x_{16} & -13.55 x_{11} & -0.10 x_{24} & +  8.83 x_{13} & -0.76 x_{29} & +  4.64 x_{10}\\
 x_{14}   &  4.81865382549 & -0.15 x_{19} & -2.78 x_{2} & -0.17 x_{30} & -0.35 x_{3} & +  1.83 x_{5} & +  0.80 x_{8} & -0.16 x_{1} & -0.21 x_{22} & -0.17 x_{20} & +  0.01 x_{16} & -0.90 x_{11} & -0.10 x_{24} & +  0.04 x_{13} & -0.15 x_{29} & +  2.47 x_{10}\\
 x_{9}   &  1.9524604557 & +  0.04 x_{19} & +  2.30 x_{2} & +  0.07 x_{30} & -0.57 x_{3} & +  0.33 x_{5} & +  0.29 x_{8} & -0.84 x_{1} & +  0.16 x_{22} & +  0.09 x_{20} & +  0.10 x_{16} & +  2.06 x_{11} & +  0.01 x_{24} & -0.20 x_{13} & +  0.11 x_{29} & -1.14 x_{10}\\
 x_{31}   &  9.84278390743 & +  0.29 x_{19} & -20.46 x_{2} & -0.67 x_{30} & -9.10 x_{3} & -15.76 x_{5} & -6.91 x_{8} & -4.28 x_{1} & -1.76 x_{22} & +  0.29 x_{20} & -0.54 x_{16} & -29.55 x_{11} & +  0.61 x_{24} & -2.65 x_{13} & -1.45 x_{29} & + 26.86 x_{10}\\
\hline
z    &  -1.64305974201 & -0.15 x_{19} & -8.95 x_{2} & -0.27 x_{30} & -1.94 x_{3} & -4.39 x_{5} & -6.42 x_{8} & -2.07 x_{1} & -0.34 x_{22} & -0.07 x_{20} & -0.32 x_{16} & -12.14 x_{11} & +  0.02 x_{24} & -0.02 x_{13} & -0.58 x_{29} & -0.23 x_{10}\\
\end{array}\]


 $ x_{24} $ enters and $ x_{18} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{4}   &  0.758271002455 & -0.13 x_{19} & -6.76 x_{2} & -0.28 x_{30} & -1.19 x_{3} & -0.02 x_{5} & +  0.72 x_{8} & -0.77 x_{1} & -0.40 x_{22} & -0.11 x_{20} & -0.06 x_{16} & -4.46 x_{11} & +  0.10 x_{18} & +  0.40 x_{13} & -0.35 x_{29} & +  4.74 x_{10}\\
 x_{17}   &  57.9213861773 & -4.02 x_{19} & -150.42 x_{2} & -6.34 x_{30} & -29.98 x_{3} & +  8.92 x_{5} & + 17.83 x_{8} & -34.20 x_{1} & -8.30 x_{22} & -2.49 x_{20} & -0.70 x_{16} & -95.58 x_{11} & +  2.39 x_{18} & +  1.20 x_{13} & -6.75 x_{29} & + 103.38 x_{10}\\
 x_{6}   &  0.702463004178 & +  0.05 x_{19} & +  0.10 x_{2} & +  0.04 x_{30} & +  0.43 x_{3} & -0.45 x_{5} & -0.15 x_{8} & +  0.33 x_{1} & -0.01 x_{22} & +  0.01 x_{20} & -0.02 x_{16} & +  0.03 x_{11} & +  0.02 x_{18} & -0.05 x_{13} & +  0.03 x_{29} & -0.09 x_{10}\\
 x_{24}   &  22.646746165 & +  1.04 x_{19} & + 77.53 x_{2} & +  1.94 x_{30} & +  4.72 x_{3} & + 15.60 x_{5} & +  8.58 x_{8} & +  2.97 x_{1} & +  4.18 x_{22} & -0.27 x_{20} & +  1.43 x_{16} & + 65.30 x_{11} & -1.22 x_{18} & -14.54 x_{13} & +  3.11 x_{29} & -46.79 x_{10}\\
 x_{26}   &  33.1444203138 & -2.28 x_{19} & -101.43 x_{2} & -2.47 x_{30} & -2.50 x_{3} & -5.75 x_{5} & -31.96 x_{8} & + 13.49 x_{1} & -5.46 x_{22} & -0.91 x_{20} & -2.12 x_{16} & -74.87 x_{11} & +  0.81 x_{18} & + 31.55 x_{13} & -4.44 x_{29} & + 63.70 x_{10}\\
 x_{21}   &  37.6318110977 & +  1.50 x_{19} & + 34.46 x_{2} & +  0.89 x_{30} & +  2.40 x_{3} & -9.07 x_{5} & -0.63 x_{8} & + 10.65 x_{1} & +  1.78 x_{22} & +  1.33 x_{20} & -0.14 x_{16} & +  5.59 x_{11} & -0.68 x_{18} & -13.93 x_{13} & +  1.50 x_{29} & -29.70 x_{10}\\
 x_{7}   &  1.61643318377 & +  0.05 x_{19} & +  1.77 x_{2} & +  0.09 x_{30} & +  0.30 x_{3} & -0.53 x_{5} & -0.59 x_{8} & +  0.04 x_{1} & +  0.16 x_{22} & +  0.07 x_{20} & -0.00 x_{16} & +  1.59 x_{11} & +  0.01 x_{18} & +  0.23 x_{13} & +  0.13 x_{29} & -1.83 x_{10}\\
 x_{23}   &  49.6527222637 & +  1.11 x_{19} & + 68.35 x_{2} & +  1.63 x_{30} & +  3.54 x_{3} & + 16.68 x_{5} & + 12.83 x_{8} & -12.35 x_{1} & +  3.58 x_{22} & +  0.08 x_{20} & +  1.04 x_{16} & + 47.69 x_{11} & -0.45 x_{18} & -10.20 x_{13} & +  3.24 x_{29} & -48.28 x_{10}\\
 x_{12}   &  0.33636402718 & -0.16 x_{19} & -5.71 x_{2} & -0.12 x_{30} & +  0.22 x_{3} & -0.76 x_{5} & -1.14 x_{8} & +  0.52 x_{1} & -0.30 x_{22} & -0.08 x_{20} & -0.10 x_{16} & -3.19 x_{11} & +  0.08 x_{18} & +  1.63 x_{13} & -0.26 x_{29} & +  3.90 x_{10}\\
 x_{15}   &  4.53310032522 & +  0.12 x_{19} & +  3.25 x_{2} & +  0.17 x_{30} & -0.13 x_{3} & -0.75 x_{5} & -1.62 x_{8} & +  0.84 x_{1} & +  0.20 x_{22} & +  0.13 x_{20} & -0.00 x_{16} & +  1.30 x_{11} & -0.08 x_{18} & +  0.17 x_{13} & +  0.14 x_{29} & -2.19 x_{10}\\
 x_{25}   &  49.693948954 & +  2.15 x_{19} & + 84.47 x_{2} & +  2.64 x_{30} & -5.79 x_{3} & + 10.23 x_{5} & -8.35 x_{8} & -7.92 x_{1} & +  5.99 x_{22} & +  2.07 x_{20} & +  1.53 x_{16} & + 67.90 x_{11} & -0.97 x_{18} & -4.74 x_{13} & +  3.91 x_{29} & -62.19 x_{10}\\
 x_{27}   &  47.7279761495 & +  0.60 x_{19} & + 16.15 x_{2} & -0.27 x_{30} & -11.81 x_{3} & -2.53 x_{5} & + 11.71 x_{8} & -4.84 x_{1} & +  0.44 x_{22} & +  0.89 x_{20} & +  0.67 x_{16} & +  1.75 x_{11} & -0.29 x_{18} & -16.47 x_{13} & +  0.13 x_{29} & -0.52 x_{10}\\
 x_{28}   &  67.9804106405 & -0.00 x_{19} & -14.23 x_{2} & -0.71 x_{30} & -10.88 x_{3} & -9.88 x_{5} & -7.76 x_{8} & -8.96 x_{1} & -1.22 x_{22} & +  0.08 x_{20} & -0.40 x_{16} & -20.17 x_{11} & +  0.12 x_{18} & + 10.30 x_{13} & -1.07 x_{29} & +  9.38 x_{10}\\
 x_{14}   &  2.63758519618 & -0.25 x_{19} & -10.25 x_{2} & -0.35 x_{30} & -0.80 x_{3} & +  0.33 x_{5} & -0.02 x_{8} & -0.44 x_{1} & -0.62 x_{22} & -0.14 x_{20} & -0.13 x_{16} & -7.19 x_{11} & +  0.12 x_{18} & +  1.44 x_{13} & -0.45 x_{29} & +  6.98 x_{10}\\
 x_{9}   &  2.14376614383 & +  0.04 x_{19} & +  2.96 x_{2} & +  0.09 x_{30} & -0.53 x_{3} & +  0.46 x_{5} & +  0.36 x_{8} & -0.82 x_{1} & +  0.19 x_{22} & +  0.09 x_{20} & +  0.11 x_{16} & +  2.61 x_{11} & -0.01 x_{18} & -0.33 x_{13} & +  0.14 x_{29} & -1.53 x_{10}\\
 x_{31}   &  23.6801575187 & +  0.93 x_{19} & + 26.91 x_{2} & +  0.51 x_{30} & -6.21 x_{3} & -6.23 x_{5} & -1.67 x_{8} & -2.47 x_{1} & +  0.79 x_{22} & +  0.13 x_{20} & +  0.33 x_{16} & + 10.35 x_{11} & -0.75 x_{18} & -11.54 x_{13} & +  0.45 x_{29} & -1.73 x_{10}\\
\hline
z    &  -1.22250997182 & -0.13 x_{19} & -7.51 x_{2} & -0.23 x_{30} & -1.86 x_{3} & -4.10 x_{5} & -6.26 x_{8} & -2.01 x_{1} & -0.26 x_{22} & -0.07 x_{20} & -0.29 x_{16} & -10.93 x_{11} & -0.02 x_{18} & -0.29 x_{13} & -0.52 x_{29} & -1.10 x_{10}\\
\end{array}\]
Final Dictionary
Solution:  -1.22250997182
Num Pivots:  12
\end{document}
